Now, in the above equation, we can see all the elements are zero in the second row of the matrix on the LHS. Therefore, A-1 does not exist.

Note: Suppose A = IA, after applying the elementary transformation, if any row or column of a matrix on LHS is zero, then A-1 does not exist.

Note: Suppose A = IA, after applying the elementary transformation, if any row or column of a matrix on LHS is zero, then A-1 does not exist.

Now, in the above equation, we can see all the elements are zero in the second row of the matrix on the LHS. Therefore, A-1 does not exist.

Direction (Q. No. 18) Choose the correct answer in the following question.

1. Matrices A and B will be inverse of each other only if

(a) AB = BA

(b) AB = BA = O

(c) AB = 0, BA = I

(d) AB = BA = I

1. Matrices A and B will be inverse of each other only if

(a) AB = BA

(b) AB = BA = O

(c) AB = 0, BA = I

(d) AB = BA = I

Sol. We know that 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 said to be the inverse of A. In this case, it is clear that A is the inverse of B. Thus, matrices A and B will be inverse of each other only if AB = BA = I. So, correct option is (d)