Question

If $A=\begin{bmatrix} {2}&{1} &{0}\\\ {0}&{2}& {1} \\\ {1}&{0}&{2}\\\ \end{bmatrix}$ then $| adj A|$ =

• A. 81
• B. 0
• C. 9
• D. 44570

Answer 1

Answer: (A)

81

Answer 2

Given, $A=\begin{bmatrix} 2 & 1 & 0 \\\ 0 & 2 & 1 \\\ 1 & 0 & 2\end{bmatrix}$
$C_{11}=4, C_{12}=1, C_{13}=-2$
$C_{21}=-2, C_{22}=4, C_{23}=1$
$C_{31}=1, C_{32}=-2, C_{33}=4$
\therefore\,\,\,\adj $(A)=\begin{bmatrix} 4 & 1 & -2 \\\ -2 & 4 & 1 \\\ 1 & -2 & 4\end{bmatrix}^{T}$
$=\begin{bmatrix}4 & -2 & 1 \\\ 1 & 4 & -2 \\\ -2 & 1 & 4\end{bmatrix}$
$\therefore |$adj $A|=4(16+2)+2(4-4)+(1+8)$
$=72+0+9=81$