COMEDK · Maths · 21. Matrices
If for any \(2 \times 2\) square matrix \(A\),\(A(\operatorname{adj} A)=\left[\begin{array}{ll}8 & 0 \\ 0 & 8\end{array}\right]\), then find the value of \(\operatorname{det}(A)\).
- A 6
- B 7
- C 8
- D 5
Answer & Solution
Correct Answer
(C) 8
Step-by-step Solution
Detailed explanation
For any square matrix \(A\) of order \(n\), the fundamental property involving the adjoint matrix is \(A(\operatorname{adj} A) = (\operatorname{det} A) I_n\), where \(I_n\) is the identity matrix of order \(n\). Given that \(A\) is a \(2 \times 2\) matrix, we have \(n = 2\).…
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