Let $A=\begin{pmatrix}1 & -1 & 1 \ 2 & 1 & -3 \ 1 & 1 & 1\end{pmatrix}$ and $B=\begin{pmatrix}4 & 2 & 2 \ -5 & 0 & \alpha \ 1 & -2 & 3\end{pmatrix}$. If $AB=10I$ then $\alpha$ = ?

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Aicharya · Accepted Answer

$A( B)=10 I$ $\Rightarrow\begin{bmatrix}1 & -1 & 1 \ 2 & 1 & -3 \ 1 & 1 & 1\end{bmatrix}\begin{bmatrix}4 & 2 & 2 \ -5 & 0 & \alpha \ 1 & -2 & 3\end{bmatrix}=\begin{bmatrix}10 & 0 & 5-\alpha \ 0 & 10 & \alpha-5 \ 0 & 0 & 5+\alpha\end{bmatrix}=10\begin{bmatrix}1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1\end{bmatrix}$ if $\alpha=5$.

Let $A=\begin{pmatrix}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{pmatrix}$ and $B=\begin{pmatrix}4 & 2 & 2 \\…

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