If $A$ is a symmetric or skew-symmetric matrix , then $A^{2}$ is

symmetric

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skew-symmetric

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Diagonal

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scalar

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Solution

The correct option is A symmetric
A is symmetric matrix
then $A_{i j} = A_{j i}$
$A^{T} = A$
and if A is skew symmetric
$A_{i j} = - A_{j i}$
$A^{T} = - A$
$A = \frac{1}{2} (A - A^{T}) + \frac{1}{2} (A + A^{T})$

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A

A^{2}

If A is a symmetric matrix and B is a skew symmetric matrix of the same order then $A^{2} + B^{2}$ is a

B

(A B A^{T})

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