Question

If A is an invertible square matrix then _________

(a) (A^T)^-1 = (A^-1)^T

(b) (A^T)^T = (A^-1)^T

(c) (A^T)^-1 = (A^-1)^-1

(d) None of the mentioned

This question was addressed to me in semester exam.

The question is from Inverse of Matrices topic in chapter Basic Structures: Sets, Functions, Sequences, Sums and Matrices of Discrete Mathematics

Answer 1

The correct option is (a) (A^T)^-1 = (A^-1)^T

The explanation is: For invertible matrix A, A^T is also inveritble.