Question

Which of the following is known as the reversal rule?

(a) (AB)^-1 = B^-1A^-1

(b) (AB)^-1 = A^-1 B^-1

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

(d) (BA)^-1 = B^-1 A

I got this question during an online exam.

I need to ask this question from Real Matrices: Symmetric, Skew-symmetric, Orthogonal Quadratic Form in section Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

Correct option is (a) (AB)^-1 = B^-1A^-1

To explain I would say: The reversal rule of matrix multiplication states that, ‘the inverse of the product of two matrices is equal to the product of their individual inverses, taken in the reverse order’.