Question

If $A$ is a $3\times 3$ invertible matrix, then $\text{adj}\left(5A\right)$ is equal to

• A. $5^2\text{adj}\left(5A\right)$
• B. None of these
• C. $5^3\text{adj}A$
• D. $5^2\text{adj}A$

Answer 1

The correct option is D $5^2\text{adj}A$

From property, we know that
$\text{adj}\left(kB\right)=k^{n-1}\text{adj}B$, where $n$ is the order of matrix $B$.
$\therefore$ $\text{adj}\left(5A\right)=5^2\text{adj}A$