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

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3 and 4 .Determinants and Matrices

easy

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

A

$A $ is a diagonal matrix

B

$A$ is a square matrix

C

$A $ is a zero matrix

D

None of these

Solution

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 $C$.

Standard 12

Mathematics

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