Question

If A = $\begin{bmatrix} 2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2 \end{bmatrix}$, then adj. (adj. A) is equal to

• A. 8 $\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$
• B. 64 $\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$
• C. 16 $\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$
• D. None of these

Answer 1

Answer: (C)

16 $\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$

Answer 2

adj (adj A) = |A|^n–2 .A

|A| = 8

adj (adj A) = 8^3–2 .A = 8A

= $\begin{bmatrix} 16 & 0 & 0 \\ 16 & 16 & 0 \\ 16 & 16 & 16 \end{bmatrix}$ = 16$\begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1 \end{bmatrix}$