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If $C$ and $D$ are two $n \times n$ non-singular matrices over the set of real number $\mathbf{R}$ such that $C D=-D C$, then $n$ is
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The correct answer is:
$n$ even integer
Given, $C$ and $D$ are non-singular matrix of order $n$
$\because \quad|C| \neq 0,|D| \neq 0$
$C D=-D C$
$|C D|=|-D C|$
$|C||D|=(-1)^n|D||C|$
$\mathrm{l}=(-1)^n$
$\therefore n$ is even integer.
$\because \quad|C| \neq 0,|D| \neq 0$
$C D=-D C$
$|C D|=|-D C|$
$|C||D|=(-1)^n|D||C|$
$\mathrm{l}=(-1)^n$
$\therefore n$ is even integer.
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