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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

  1. A \(-2\)
  2. B \(-4\)
  3. C 4
  4. D 8
Verified Solution

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…