Let $B=\left(\begin{array}{ccc}2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1\end{array} ight)$ and $C=\left(\begin{array}{ccc}-1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2\end{array} ight)$ If a matrix $A$ is such that $\mathrm{BAC}=\mathrm{I}$, then $\mathrm{A}^{-1}=$

Question

Let $B=\left(\begin{array}{ccc}2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1\end{array}ight)$ and $C=\left(\begin{array}{ccc}-1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2\end{array}ight)$ If a matrix $A$ is such that $\mathrm{BAC}=\mathrm{I}$, then $\mathrm{A}^{-1}=$

Aicharya · Accepted Answer

$\begin{aligned} & 	ext {Given BAC }=1 \ & \Rightarrow(B A)^{-1}=C \ & \Rightarrow A^{-1} B^{-1}=C \Rightarrow A^{-1}=C B \ & \Rightarrow A^{-1}=\left[\begin{array}{ccc}-1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2\end{array}ight]\left[\begin{array}{ccc}2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1\end{array}ight]=\left[\begin{array}{ccc}-3 & -5 & -5 \ 0 & 9 & 2 \ 2 & 14 & 6\end{array}ight]\end{aligned}$

Let $B=\left(\begin{array}{ccc}2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & 1 & -1\end{array}\right)$ and…

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