KCET · Maths · Matrices
If \(\mathrm{A}(\operatorname{adj} \mathrm{A})=5 \mathrm{I}\) where \(I\) is the identity matrix of order 3 , then \(\mid\) adj \(A \mid\) is equal to
- A 125
- B 25
- C 5
- D 10
Answer & Solution
Correct Answer
(B) 25
Step-by-step Solution
Detailed explanation
Given, \(A(\operatorname{adj} A)=5 I\)
\[
\begin{aligned}
&\therefore \quad|\mathrm{A}| \mathrm{I}=5 \mathrm{I} \Rightarrow|\mathrm{A}|=5 \\
&\therefore \quad|\operatorname{adj}(\mathrm{A})|=|\mathrm{A}|^{3-1}=|\mathrm{A}|^{2}=(5)^{2}=25
\end{aligned}
\]
\[
\begin{aligned}
&\therefore \quad|\mathrm{A}| \mathrm{I}=5 \mathrm{I} \Rightarrow|\mathrm{A}|=5 \\
&\therefore \quad|\operatorname{adj}(\mathrm{A})|=|\mathrm{A}|^{3-1}=|\mathrm{A}|^{2}=(5)^{2}=25
\end{aligned}
\]
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