Question

Which of the following is true for matrices?

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

(b) (A^T) = A

(c) AB = BA

(d) A*I = I

This question was addressed to me during a job interview.

This interesting question is from Transformation (Reduction) of Quadratic Form to Canonical Form topic in portion Eigen Values and Eigen Vectors of Engineering Mathematics

Answer 1

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

The explanation is: The correct forms of the other options are:

(A^T)^T = A

 AB ≠ BA

 A*I = A