Math Linear Algebra

Question

If A and B are real symmetric matrices of size n*n. Then, which one of the following is true?

a) AA^t = I

b) A = A^-1

c) AB =BA

d) (AB)^t = BA

Answer 1

Correct option is D.

By various theorems and properties,

$$(A.B)^t = B^t.A^t = B.A$$

[As $A$ and $B$ are symmetric matrices, $A^t = A$ and $B^t = B$. ]