Question

If a matrix A is both symmetric and skew symmetric, then

• A. A is diagonal matrix
• B. A is a zero matrix
• C. A is scalar matrix
• D. A is square matrix

Answer 1

The correct option is B A is a zero matrix

If matrix A is symmetric
$A^T=A$
If matrix A is skew symmetric
$A^T=-A$
Also, diagonal elements are zero
Now, it is given that a matrix A is both symmetric as well as skew symmetric
$\therefore A=A^T=-A$
which is only possible if A is zero matrix
$A=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]=A^T=-A$
Therefore option B is correct answer