NCERT Solutions Class-12-Chapter-3-Matrices
Excercise-3.4
Note: A square matrix \( A \) is said to be invertible if there exists another square matrix \( B \) of the same order such that their product is the Identity Matrix \( I \). In this case, \( B \) is called the inverse of \( A \).
Q1
Matrices A and B will be inverse of each other only if- \( AB = BA \)
- \( AB = BA = 0 \)
- \( AB = 0, BA = I \)
- \( AB = BA = I \)
- \( AB = BA \)
- \( AB = BA = 0 \)
- \( AB = 0, BA = I \)
- \( AB = BA = I \)
Answer: (D)
Solution:
By the definition of invertible matrices:
If \( A \) is a square matrix of order \( m \), and if there exists another square matrix \( B \) of the same order \( m \), such that \( AB = BA = I \), then \( B \) is called the inverse matrix of \( A \) and is denoted by \( A^{-1} \).
Thus, matrices A and B are inverses of each other if and only if \( AB = BA = I \).
Therefore, the correct option is (D).