How many practice questions are available for Matrices?

SparkEd Math offers 60+ practice questions for Matrices across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Matrices content free on SparkEd Math?

Yes! All Matrices content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Matrices differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Matrices problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Matrices content aligned with the ICSE syllabus?

Yes, all Matrices questions and lessons on SparkEd Math are fully aligned with the Indian Certificate of Secondary Education (ICSE) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Matrices — Class 10 ICSE (2025-26)

About Matrices — Class 10 ICSE

Perform matrix operations including addition, subtraction, and multiplication of 2x2 matrices. This topic is part of the ICSE Class 10 mathematics syllabus (chapter: Chapter 10). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 25-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Matrices

Introduction to Matrices: Organizing Data Systematically
Matrix Addition and Subtraction: Combining Data
Scalar Multiplication: Scaling Matrix Values
Matrix Multiplication: The 'Row by Column' Rule
Summary, Special Matrices & Exam Preparation

Interactive lesson · about 15 minutes · checkpoint question after every unit

Matrices — solved examples for Class 10 ICSE

Example 1easy

What is the order of the matrix

A = \begin{pmatrix} 3 & 5 \\ 4 & -2 \end{pmatrix}

A) $1 \times 2$
B) $2 \times 1$
C) $2 \times 2$
D) $4 \times 1$

Step-by-step solution

Count rows: 2 rows (horizontal lines of numbers).
Count columns: 2 columns (vertical lines of numbers).
Order = rows x columns
$= 2 \times 2$

Answer: $2 \times 2$

Example 2medium

A = \begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}

and

B = \begin{pmatrix} 2 & 1 \\ 1 & 2 \end{pmatrix}

, find

A(BA)

A) $\begin{pmatrix} 22 & 21 \\ 21 & 22 \end{pmatrix}$
B) $\begin{pmatrix} 21 & 22 \\ 22 & 21 \end{pmatrix}$
C) $\begin{pmatrix} 20 & 23 \\ 23 & 20 \end{pmatrix}$
D) $\begin{pmatrix} 22 & 22 \\ 21 & 21 \end{pmatrix}$

Step-by-step solution

Find $BA$ :
$BA = \begin{pmatrix} 2(1)+1(2) & 2(2)+1(1) \\ 1(1)+2(2) & 1(2)+2(1) \end{pmatrix} = \begin{pmatrix} 4 & 5 \\ 5 & 4 \end{pmatrix}$
Find $A(BA)$ :
$A \begin{pmatrix} 4 & 5 \\ 5 & 4 \end{pmatrix} = \begin{pmatrix} 1(4)+2(5) & 1(5)+2(4) \\ 2(4)+1(5) & 2(5)+1(4) \end{pmatrix}$
Result:
$= \begin{pmatrix} 14 & 13 \\ 13 & 14 \end{pmatrix}$

Answer: $\begin{pmatrix} 22 & 21 \\ 21 & 22 \end{pmatrix}$

Example 3hard

X = \begin{pmatrix} 4 & 1 \\ -1 & 2 \end{pmatrix}

, show that

6X - X^2 = 9I

. What is

X^2

A) $\begin{pmatrix} 15 & 6 \\ -6 & 3 \end{pmatrix}$
B) $\begin{pmatrix} 16 & 6 \\ -6 & 4 \end{pmatrix}$
C) $\begin{pmatrix} 15 & 6 \\ 6 & 3 \end{pmatrix}$
D) $\begin{pmatrix} 17 & 6 \\ -6 & 3 \end{pmatrix}$

Step-by-step solution

$X^2 = X \times X$ :
(1,1):
$4(4) + 1(-1) = 15$
(1,2):
$4(1) + 1(2) = 6$
(2,1):
$-1(4) + 2(-1) = -6$
(2,2):
$-1(1) + 2(2) = 3$
So $X^2 = \begin{pmatrix} 15 & 6 \\ -6 & 3 \end{pmatrix}$
Verify:
$6X - X^2 = \begin{pmatrix} 24-15 & 6-6 \\ -6+6 & 12-3 \end{pmatrix} = \begin{pmatrix} 9 & 0 \\ 0 & 9 \end{pmatrix} = 9I \; \checkmark$

Answer: $\begin{pmatrix} 15 & 6 \\ -6 & 3 \end{pmatrix}$

Practice questions on Matrices

Q1.easy
If $A = \begin{pmatrix} 2 & 5 \\ 1 & 3 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 1 \\ 2 & 6 \end{pmatrix}$ , find $A + B$ .
1. A) $\begin{pmatrix} 6 & 6 \\ 3 & 9 \end{pmatrix}$
2. B) $\begin{pmatrix} 6 & 4 \\ 3 & 9 \end{pmatrix}$
3. C) $\begin{pmatrix} 6 & 6 \\ 2 & 9 \end{pmatrix}$
4. D) $\begin{pmatrix} 8 & 6 \\ 3 & 9 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 6 & 6 \\ 3 & 9 \end{pmatrix}$
Hint: Add corresponding elements: top-left + top-left, top-right + top-right, etc.
Q2.easy
If $A = \begin{pmatrix} 7 & 2 \\ 3 & 8 \end{pmatrix}$ and $B = \begin{pmatrix} 4 & 1 \\ 2 & 5 \end{pmatrix}$ , find $A - B$ .
1. A) $\begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix}$
2. B) $\begin{pmatrix} 3 & 3 \\ 1 & 3 \end{pmatrix}$
3. C) $\begin{pmatrix} 11 & 3 \\ 5 & 13 \end{pmatrix}$
4. D) $\begin{pmatrix} 3 & 1 \\ 5 & 3 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 3 & 1 \\ 1 & 3 \end{pmatrix}$
Hint: Subtract corresponding elements of B from A.
Q3.easy
Find $3A$ if $A = \begin{pmatrix} 2 & -1 \\ 4 & 5 \end{pmatrix}$ .
1. A) $\begin{pmatrix} 6 & -3 \\ 12 & 15 \end{pmatrix}$
2. B) $\begin{pmatrix} 6 & -1 \\ 12 & 15 \end{pmatrix}$
3. C) $\begin{pmatrix} 6 & -3 \\ 4 & 15 \end{pmatrix}$
4. D) $\begin{pmatrix} 5 & 2 \\ 7 & 8 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 6 & -3 \\ 12 & 15 \end{pmatrix}$
Hint: Multiply every element of A by 3.
Q4.medium
If $A = \begin{pmatrix} 1 & -2 \\ 2 & -1 \end{pmatrix}$ and $B = \begin{pmatrix} 3 & 2 \\ -2 & 1 \end{pmatrix}$ , find $2B - A^2$ .
1. A) $\begin{pmatrix} 3 & 4 \\ -4 & -1 \end{pmatrix}$
2. B) $\begin{pmatrix} 9 & 4 \\ -4 & 5 \end{pmatrix}$
3. C) $\begin{pmatrix} 3 & 4 \\ 4 & -1 \end{pmatrix}$
4. D) $\begin{pmatrix} 3 & -4 \\ -4 & -1 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 3 & 4 \\ -4 & -1 \end{pmatrix}$
Hint: Find $A^2$ first, then $2B$ , then subtract.
Q5.medium
If $A = \begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$ , $B = \begin{pmatrix} 2 & 1 \\ 4 & 2 \end{pmatrix}$ and $C = \begin{pmatrix} 5 & 1 \\ 7 & 4 \end{pmatrix}$ , compute $A(B + C)$ .
1. A) $\begin{pmatrix} 29 & 15 \\ 65 & 33 \end{pmatrix}$
2. B) $\begin{pmatrix} 29 & 33 \\ 65 & 15 \end{pmatrix}$
3. C) $\begin{pmatrix} 15 & 29 \\ 33 & 65 \end{pmatrix}$
4. D) $\begin{pmatrix} 29 & 15 \\ 33 & 65 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 29 & 15 \\ 65 & 33 \end{pmatrix}$
Hint: First compute $B + C$ , then multiply $A$ by the result.
Q6.medium
If $A = \begin{pmatrix} 2 & 1 \\ 0 & -2 \end{pmatrix}$ , $B = \begin{pmatrix} 4 & 1 \\ -3 & -2 \end{pmatrix}$ and $C = \begin{pmatrix} -3 & 2 \\ -1 & 4 \end{pmatrix}$ , find $A^2 + AC - 5B$ .
1. A) $\begin{pmatrix} -14 & 2 \\ 17 & 6 \end{pmatrix}$
2. B) $\begin{pmatrix} -14 & -2 \\ 17 & 6 \end{pmatrix}$
3. C) $\begin{pmatrix} 14 & 2 \\ -17 & 6 \end{pmatrix}$
4. D) $\begin{pmatrix} -14 & 2 \\ 17 & -6 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} -14 & 2 \\ 17 & 6 \end{pmatrix}$
Hint: Calculate $A^2$ , $AC$ , and $5B$ separately, then combine.
Q7.hard
Show that $\begin{pmatrix} 1 & 2 \\ 2 & 1 \end{pmatrix}$ is a solution of $X^2 - 2X - 3I = O$ . What is $X^2 - 2X$ ?
1. A) $\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}$
2. B) $\begin{pmatrix} 3 & 2 \\ 2 & 3 \end{pmatrix}$
3. C) $\begin{pmatrix} -3 & 0 \\ 0 & -3 \end{pmatrix}$
4. D) $\begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 3 & 0 \\ 0 & 3 \end{pmatrix}$
Hint: If $X^2 - 2X - 3I = O$ , then $X^2 - 2X = 3I$ .
Q8.hard
If $A = \begin{pmatrix} 4 & -4 \\ -4 & 4 \end{pmatrix}$ , find $A^2$ . If $A^2 = pA$ , find $p$ .
1. A) $p = 8$
2. B) $p = 4$
3. C) $p = 16$
4. D) $p = 2$
Show answer
Answer: $p = 8$
Hint: Compute $A^2$ , then compare with $pA$ element by element.
Q9.hard
If $A = \begin{pmatrix} 3 & -4 \\ -1 & 2 \end{pmatrix}$ , find matrix $B$ such that $BA = I$ (identity matrix). What is $B$ ?
1. A) $\begin{pmatrix} 1 & 2 \\ \frac{1}{2} & \frac{3}{2} \end{pmatrix}$
2. B) $\begin{pmatrix} 2 & 4 \\ 1 & 3 \end{pmatrix}$
3. C) $\begin{pmatrix} 2 & -4 \\ 1 & -3 \end{pmatrix}$
4. D) $\begin{pmatrix} -2 & -4 \\ -1 & -3 \end{pmatrix}$
Show answer
Answer: $\begin{pmatrix} 1 & 2 \\ \frac{1}{2} & \frac{3}{2} \end{pmatrix}$
Hint: Let $B = \begin{pmatrix} a & b \\ c & d \end{pmatrix}$ . Then $BA = I$ gives 4 equations.

These are 9 of the 60 questions available for Matrices. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.