Anand Classes presents well-structured and accurate NCERT Solutions for Matrices Exercise 3.4 of Class 12 Math Chapter 3, designed to help students strengthen their understanding of matrix operations and concepts. These solutions follow the latest CBSE guidelines and provide step-by-step explanations to improve conceptual clarity and exam performance. Perfect for board exam preparation, competitive exams, and revision sessions, these notes ensure students can learn effectively and score higher. Click the print button to download study material and notes.
Access NCERT Solutions for Matrices Exercise 3.4 of Class 12 Math Chapter 3
NCERT Question 1 : Matrices $A$ and $B$ will be inverse of each other only if:
(A) $(AB = BA)$
(B) $(AB = BA = 0)$
(C) $(AB = 0, BA = I)$
(D) $(AB = BA = I)$
Solution
For two matrices $A$ and $B$ to be inverses of each other, the definition of an inverse matrix states:
$$AB = BA = I.$$
This means:
- Their product must give the identity matrix.
- The product must be the identity in both orders.
Therefore, the condition for $A$ and $B$ to be inverses is:
$$AB = BA = I.$$
So the correct option is:
$$
\boxed{(D)}
$$
Here is a simple and clear explanation with an example to show when two matrices are inverses of each other.
When are two matrices inverses?
Two matrices $A$ and $B$ are inverse of each other only if:
$$AB = BA = I$$
where (I) is the identity matrix.
This means:
- Multiply $A$ and $B$ (in both orders).
- If both products give the identity matrix, then $A$ and $B$ are inverses.
Example
Let
$$
A=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix},
\qquad
B=\begin{bmatrix}2 & -3 \\ -1 & 2\end{bmatrix}
$$
We will check whether (A) and (B) are inverses.
Step 1: Compute $AB$
$$
AB=\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix}
\begin{bmatrix}2 & -3 \\ -1 & 2\end{bmatrix}
$$
Multiply:
- First row × first column: $(2\cdot 2 + 3\cdot (-1)= 4 – 3 = 1)$
- First row × second column: $(2\cdot (-3) + 3\cdot 2 = -6 + 6 = 0)$
- Second row × first column: $(1\cdot 2 + 2\cdot (-1) = 2 – 2 = 0)$
- Second row × second column: $(1\cdot (-3) + 2\cdot 2 = -3 + 4 = 1)$
Thus,
$$
AB=\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}=I
$$
Step 2: Compute (BA)
$$
BA=\begin{bmatrix}2 & -3 \\ -1 & 2\end{bmatrix}
\begin{bmatrix}2 & 3 \\ 1 & 2\end{bmatrix}
$$
Multiply:
- First row × first column: $(2\cdot 2 + (-3)\cdot 1 = 4 – 3 = 1)$
- First row × second column: $(2\cdot 3 + (-3)\cdot 2 = 6 – 6 = 0)$
- Second row × first column: $((-1)\cdot 2 + 2\cdot 1 = -2 + 2 = 0)$
- Second row × second column: $((-1)\cdot 3 + 2\cdot 2 = -3 + 4 = 1)$
Thus,
$$
BA=\begin{bmatrix}1 & 0 \\ 0 & 1\end{bmatrix}=I
$$
✔ Both (AB) and (BA) equal the identity matrix.
So:
$$
A^{-1} = B \quad \text{and} \quad B^{-1} = A
$$
Hence, A and B are inverses of each other.
For more clear and accurate NCERT Class 12 solutions, you can explore the step-wise explanations and matrix concepts available through Anand Classes — perfect for CBSE board revision and building strong fundamentals in Matrices and Determinants.
✅ FAQ Section
Q1. What is covered in Matrices Exercise 3.4 of Class 12 Chapter 3?
Exercise 3.4 mainly focuses on the multiplication of matrices and properties associated with matrix multiplication. Students learn how to solve matrix equations and apply rules effectively.
Q2. Are these NCERT Solutions for Matrices Exercise 3.4 updated as per the latest CBSE syllabus?
Yes, all solutions provided are fully updated according to the latest CBSE curriculum and NCERT guidelines for Class 12.
Q3. How do these solutions help in Class 12 board exam preparation?
The step-by-step solutions help students understand concepts clearly, improving accuracy and speed—both essential for scoring high in board exams.
Q4. Can I download Matrices Exercise 3.4 NCERT Solutions as a PDF?
Yes, you can easily download the complete solutions in PDF format for free and use them for offline study.
Q5. Who has prepared these Matrices NCERT Solutions?
These solutions are prepared by subject experts at Anand Classes, known for delivering high-quality study material for Class 12 Mathematics.
