Question

Show that A’A and AA’ are both symmetric matrices for any matrix A.

Answer 1

Let P = A'A

∴ P'= (A'A)'

= A'(A')' [∵ (AB)' = B'A']

So, A'A is symmetrice matrix for any matrix A.

Now, let Q = AA'

∴ Q' = (AA')' = (A')'(A)' = AA' = Q

So, AA' is symmetric matrix for any matrix A.