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# A skew-symmetric matrix S satisfies the relation $S^2+I=0$ where $I$ is a unit matrix. Then $SS'$ is equal to

$(a)\;I\qquad(b)\;2I\qquad(c)\;-I\qquad(d)\;None\;of\;these$

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## 1 Answer

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Since $S$ is skew-symmetric matrix $S'=-S$
We have $S^2+I=0$
$S^2=-I+0$
$\quad\;=-I$
$S.S=-I$
$\Rightarrow S.S.S'=-IS'$
$\qquad\qquad=I(-S')$
$\qquad\qquad=IS$
$\qquad\qquad=S$
$S^{-1}SSS'=S^{-1}S$
(i.e) $ISS'=I$
$SS'=I$
$\Rightarrow$ If $SS'=I$ then $S$ is said to be an orthogonal matrix.
Hence (a) is the correct answer.
answered Nov 25, 2013

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