Show that A′A and AA′ are both symmetric matrices for any matrix … - Vidyadip

Question

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

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Answer

Let P = A'A
$\therefore$ P' = (AA')'
= A'(A')' $[\because$ (AB')' = BA'$]$
= A'A = P
So, A’A is symmetric matrix for any matrix A.
Similarly, let Q = AA’
$\therefore$ Q' = (AA')' = (A')'(A)'
= A(A')' = Q
So, AA’ is symmetric matrix for any matrix A.

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