# NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.4

These NCERT Solutions for Class 12 Maths Chapter 3 Matrices Ex 3.4 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 12 Maths Chapter 3 Matrices Exercise 3.4

Question 1.
$$\begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 1 & -1 \\ 2 & 3 \end{bmatrix}$$
Write
A = IA

Question 2.
$$\begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & 1 \\ 1 & 1 \end{bmatrix}$$
Write
A = IA

Question 3.
$$\begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 1 & 3 \\ 2 & 7 \end{bmatrix}$$
Write
A = IA

Question 4.
$$\begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & 3 \\ 5 & 7 \end{bmatrix}$$
Write
A = IA

Question 5.
$$\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & 1 \\ 7 & 4 \end{bmatrix}$$
Write
A = IA

Question 6.
$$\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$$
Write
A = IA

Question 7.
$$\begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 3 & 1 \\ 5 & 2 \end{bmatrix}$$
Write
A = IA

Question 8.
$$\begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 4 & 5 \\ 3 & 4 \end{bmatrix}$$
Write
A = IA

Question 9.
$$\begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 3 & 10 \\ 2 & 7 \end{bmatrix}$$
Write
A = IA

Question 10.
$$\begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 3 & -1 \\ -4 & 2 \end{bmatrix}$$
Write
A = IA

Question 11.
$$\begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix}$$
Write
A = IA

Question 12.
$$\begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix}$$
To use column transformation write A = AI
$$\begin{bmatrix} 6 & -3 \\ -2 & 1 \end{bmatrix}$$ = A$$\left[\begin{array}{ll} 1 & 0 \\ 0 & 1 \end{array}\right]$$
Applying C1 → C1 + 2C2
$$\left[\begin{array}{ll} 0 & -3 \\ 0 & 1 \end{array}\right]$$ = A$$\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right]$$

Question 13.
$$\begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & -3 \\ -1 & 2 \end{bmatrix}$$
Write
A = IA

Question 14.
$$\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$$
Solution:
Let $$A=\begin{bmatrix} 2 & 1 \\ 4 & 2 \end{bmatrix}$$
Write
A = IA

Question 15.
$$\left[ \begin{matrix} 2 & -3 & 3 \\ 2 & 2 & 3 \\ 3 & -2 & 2 \end{matrix} \right]$$
Solution:

Question 16.
$$\left[ \begin{matrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 2 \end{matrix} \right]$$
Solution:

Question 17.
$$\left[ \begin{matrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{matrix} \right]$$
Solution:
Row transformation
Let $$A=\left[ \begin{matrix} 2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3 \end{matrix} \right]$$

Question 18.
Choose the correct answer in the following question:
Matrices A and B will be inverse of each other only if
(a) AB = BA
(b) AB = BA = 0
(c) AB = 0, BA = 1
(d) AB = BA = I
Solution:
Choice (d) is correct
i.e., AB = BA = I

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