Question

If \(A = \begin{bmatrix} 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 \end{bmatrix}\), find the value of the matrix expression \(A(I + \text{adj } A)\), where \(I\) is the identity matrix of the same order as \(A\).

• A. \( \begin{bmatrix} 8 & -2 & 2 0 & 8 & -3 3 & -2 & 8 \end{bmatrix} \)
• B. \( \begin{bmatrix} 9 & -2 & 2 0 & 10 & -3 3 & -2 & 12 \end{bmatrix} \)
• C. \( \begin{bmatrix} 1 & -16 & 16 0 & 16 & -24 24 & -16 & 32 \end{bmatrix} \)
• D. \( \begin{bmatrix} 9 & 0 & 0 0 & 10 & 0 0 & 0 & 12 \end{bmatrix} \)

Hint:

Always replace \(A\cdot \text{adj}(A)\) with \(|A|I\). It saves time and avoids the heavy computation of cofactors in higher-order matrices.

Answer 1

The Correct Option is B