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  4. A skew-symmetric matrix S satisfies the relation S2+I=0, where I is a unit matrix; then S is

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

Matrices

Solution:

As $S$ is skew-symmetric, $S^{T}=-S$.
We have $S^{2}+I=O$
$\Rightarrow S^{2}=-I$
or $S S=-I$
$\Rightarrow S(-S)=I$
$\Rightarrow S S^{T}=I$