COMEDK · Maths · 21. Matrices
If \(A(\operatorname{adj} A)=\left[\begin{array}{ccc}-2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2\end{array}\right]\), then \(|\operatorname{adj} A|\) equals
- A \(-2\)
- B \(-4\)
- C 4
- D 8
Answer & Solution
Correct Answer
(C) 4
Step-by-step Solution
Detailed explanation
Given \(A(\operatorname{adj} A) = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix} = -2I\), where \(I\) is the \(3 \times 3\) identity matrix. Using the property \(A(\operatorname{adj} A) = |A|I\), we have \(|A| = -2\). The determinant of the adjoint of a…
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