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Skew Symmetric Matrix

A skew-symmet...

Question

$A$ skew-symmetric matrix $A$ satisfies the relation $A^{2} + I = 0$ , where $I$ is a unit matrix then $A$ is

idempotent

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orthogonal

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of even order

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odd order

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Solution

The correct options are
B orthogonal
C of even order
Given: $A^{2} + I = 0$
$\Rightarrow A^{2} = - I$
Property of orthogonal matrix $A^{2} = I$ if $A$ is of odd order and
$A^{2} = - I$ if $A$ is of even order.
Hence, $A$ is an orthogonal matrix of even order.

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