Question

Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to

• A. $\mid A\mid$
• B. $\mid A\mid2$
• C. $\mid A\mid3$
• D. $3\mid A\mid$

Answer 1

Answer: (B)

$\mid A\mid2$

Answer 2

We know that
(adj A)A=$\mid A\mid I$=$\begin{bmatrix}\mid A\mid &0&0\\\0&\mid A\mid& 0\\\0&0&\mid A\mid\end{bmatrix}$

\Rightarrow $$\mid adjA)A\mid=$\begin{vmatrix}\mid A\mid &0&0\\\0&\mid A\mid& 0\\\0&0&\mid A\mid\end{vmatrix}$

$\Rightarrow \mid adjA \mid A\mid \mid$=IAI3 $\begin{vmatrix}1&0&0\\\0&1& 0\\\0&0&1\end{vmatrix}$=$\mid A \mid^3(I)$
$\therefore \mid adjA \mid= \mid A \mid^2$

Hence, the correct answer is B