Question

A skew-symmetric matrix $M$ satisfies the relation $M^2+I=0$, 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

The correct option is A $I$

Since, $M$ is skew-symmetric matrix.

Therefore, $M^{\prime }=-M$

Also, $M^2+I=0$

$\Rightarrow M^2=-I+0=-I$

$\Rightarrow M\cdot M=-I$

$\Rightarrow MM{M}^{\prime }=-I{M}^{\prime }=-I(-M)=IM=M$

$\Rightarrow M^{-1}MM{M}^{\prime }=M^{-1}M$

$\Rightarrow IM{M}^{\prime }=I$

$\Rightarrow M{M}^{\prime }=I$