Question

A skew-symmetric matrix $M$ satisfies the relation $M+I=0$ , where $I$ is the unit matrix. Then, $M{M}^{\prime }$ is equal to

• A. $I$
• B. $2I$
• C. $-I$
• D. None of these

Answer 1

Answer: (A)

Since, $M$ is skew-symmetric matrix
$M^{\prime }=-M$ Also, $M^2+I=0$
$\Rightarrow$ $M^2=-I+0=-I$
$\Rightarrow$ $M\cdot M=-I$
$\Rightarrow$ $MM{M}^{\prime }=I{M}^{\prime }=I(-M^{\prime })=IM=M$
$\Rightarrow$ $M^{-1}MM{M}^{\prime }=M^{-1}M$
$\Rightarrow$ $IM{M}^{\prime }=I$
$\Rightarrow$ $M{M}^{\prime }=I$