Let A = [ ccc 1 & -1 & 1 2 & 1 & -3 1 & 1 & 1 ] and 10 B= [ ccc 4… - Vidyadip

MCQ

Let $A =\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$ and $10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]$. If B is the inverse of matrix A , then $\alpha$ is

A
$0$
B
1
C
2
✓
5

✓

Answer

Correct option: D.

5

(D) $10 A^{-1}=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] \quad \ldots\left[\because B = A ^{-1}\right]$
$\Rightarrow 10 A^{-1} A=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right] A$
$\Rightarrow 10 I =\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right]$
$\Rightarrow\left[\begin{array}{ccc}10 & 0 & 0 \\ 0 & 10 & 0 \\ 0 & 0 & 10\end{array}\right]=\left[\begin{array}{ccc}10 & 0 & 0 \\ -5+\alpha & 5+\alpha & -5+\alpha \\ 0 & 0 & 10\end{array}\right]$
$\therefore \quad-5+\alpha=0 \Rightarrow \alpha=5$

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