Question

Which among the following is listed under the law of transposes?

(a) (A^T)^T = A^I

(b) (A*)* = A*

(c) (cA)^T = cA^T

(d) (AB)^T = A^TB^T

This question was addressed to me in an interview.

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

Answer 1

The correct answer is (c) (cA)^T = cA^T

The best explanation: The following are listed under the law of transposes:

(A*)* = A

(A^T)^T = A

(AB)^T = B^T A^T

(cA)^T = cA^T

(A ± B)^T = A^T ± B^T (and for ∗)

If A is symmetric, A = A^T