Question

Choose the correct answer in the following question:
If a matrix A is both symmetric and skew-symmetric matrix, then
(a)A is a diagonal matrix
(b)A is zero matrix
(c)A is a square matrix
(d)None of these

Answer 1

Let A be a square matrix such that A is both symmetric and skew-symmetric matrix.
$\Rightarrow A^{\prime }=A(\because$ A is symmetric)
and $A^{\prime }=-A(\because$ Ais skew-symmetric)
$\therefore A=-A\Rightarrow A+A=0\Rightarrow 2A=0\Rightarrow A=0$
$\therefore$ Hence, (b)is the correct option