Question

A square matrix $A$ is said to be orthogonal if $A^{\prime }A=A{A}^{\prime }=I_n$

If $A$ and $B$ are orthogonal matrices, of the same size, then which one of the following is an orthogonal matrix

• A. $AB$
• B. $A+B$
• C. $A+iB$
• D. $i(A+B)$

Answer 1

The correct option is A $AB$

$\left(AB{)}^{\prime }\right(AB)=(B{}^{\prime }{A}^{\prime }\left)\right(AB)$
$=B{}^{\prime }\left(A^{\prime }A\right)B=B{}^{\prime }{I}_{n}B=BB{}^{\prime }=I_n$