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If $M$ is any square matrix of order 3 over $R$. and if $M^{\prime}$ be the transpose of $M$, then $adj\left(M^{\prime}\right)-(\text { adj } M)^{\prime}$ is equal to
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Verified Answer
The correct answer is:
null matrix
$$
\begin{aligned}
&\begin{aligned}
\text { Since, } \operatorname{adj}\left(M^{\prime}\right)=&(\operatorname{adj} M)^{\prime} \\
=& \operatorname{adj}\left(M^{\prime}\right)-(\operatorname{adj} M)^{\prime} \\
&\left[\because \operatorname{adj}\left(A^{\prime}\right)=(\operatorname{adj} A)^{\prime}\right]
\end{aligned}\\
&=0 \text { , a null matrix. }
\end{aligned}
$$
\begin{aligned}
&\begin{aligned}
\text { Since, } \operatorname{adj}\left(M^{\prime}\right)=&(\operatorname{adj} M)^{\prime} \\
=& \operatorname{adj}\left(M^{\prime}\right)-(\operatorname{adj} M)^{\prime} \\
&\left[\because \operatorname{adj}\left(A^{\prime}\right)=(\operatorname{adj} A)^{\prime}\right]
\end{aligned}\\
&=0 \text { , a null matrix. }
\end{aligned}
$$
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