If the matrix A is both symmetric and skew symmetric, then - Vidyadip

MCQ

If the matrix $\mathrm{A}$ is both symmetric and skew symmetric, then

A
$A $ is a diagonal matrix
B
$A$ is a square matrix
✓
$A $ is a zero matrix
D
None of these

✓

Answer

Correct option: C.

$A $ is a zero matrix

c
If $A$ is both symmetric and skew - symmetric matrix, then we should have $A^{\prime}=A$ and $A^{\prime}=-A$

$\Rightarrow A=-A$

$\Rightarrow A+A=0$

$\Rightarrow 2 A=0$

$\Rightarrow A=0$

Therefore, $A$ is a zero matrix.

Hence, the correct answer is $C$.

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