Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to
Let A be a nonsingular square matrix of order 3×3.Then IadjAI is equal to
\(\mid A\mid\)
\(\mid A\mid2\)
\(\mid A\mid3\)
\(3\mid A\mid\)
The Correct Option is B
Solution and Explanation
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
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