Question

For a matrix A, B and identity matrix I, if a matrix AB=I=BA then?

(a) B is inverse of A

(b) A is inverse of B

(c) A^-1 = B, B^-1 = A

(d) All of the mentioned

The question was asked during an interview.

I'd like to ask this question from Inverse of Matrices topic in portion Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

Right option is (d) All of the mentioned

Easy explanation: Since AB = I, A = B^-1 Similarly A is the inverse of B.