If $A=\begin{bmatrix}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2\end{bmatrix}$, then $\text{adj}(\text{adj} A)$ is…
If $A=\begin{bmatrix}2 & 0 & 0 \\ 2 & 2 & 0 \\ 2 & 2 & 2\end{bmatrix}$, then $\text{adj}(\text{adj} A)$ is equal to -
- \(8\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
- \(16\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
- \(64\left[\begin{array}{lll}1 & 0 & 0 \\ 1 & 1 & 0 \\ 1 & 1 & 1\end{array}\right]\)
- None of these
Solution
$|A|=\begin{bmatrix}
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{bmatrix}=(2)(2)(2)=8$
Now adj $(\text{adj} A)=|A|^{3-2} A$
$=8\begin{bmatrix}
2 & 0 & 0 \\
2 & 2 & 0 \\
2 & 2 & 2
\end{bmatrix}=16\begin{bmatrix}
1 & 0 & 0 \\
1 & 1 & 0 \\
1 & 1 & 1
\end{bmatrix}$
Asked in: TEST SERIES MHT-CET Full Test 6
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