Question:
Matrices A and B will be inverse of each other only if
A. AB = BA
C. AB = 0, BA = I
B. AB = BA = 0
D. AB = BA = I
Solution:
Answer: D
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 inverses of each other only if AB = BA = I.
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