Question

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 =O
(c)AB=O, BA=I
(d)AB=BA =I

Answer 1

We know that if A is a square matirx 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).