Question

If $M$ is any square matrix of order $3$ over $R$ and if $M^{\prime }$ be the transpose of $M$, then $\text{adj}\left(M^{\prime }\right)-\text{adj}(M{)}^{\prime }$ is equal to

• A. $M$
• B. $M^{\prime }$
• C. null matrix
• D. identity matrix

Answer 1

The correct option is C null matrix

$M^{\prime }$ be the transpose of $M$
$\Rightarrow \text{adj}\left(M^{\prime }\right)=(\text{adj}M{)}^{\prime }$
$\Rightarrow \text{adj}\left(M^{\prime }\right)-(\text{adj}M{)}^{\prime }=O$
i.e., null matrix