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

The Correct Option is B

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