If $(B A)^{-1}=C$ where $B=\left[\begin{array}{ccc}2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1\end{array} ight]$ and $C=\left[\begin{array}{ccc}-1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2\end{array} ight]$, then $A^{-1}$ is given by

Question

If $(B A)^{-1}=C$ where $B=\left[\begin{array}{ccc}2 & 6 & 4 \ 1 & 0 & 1 \ -1 & 1 & -1\end{array}ight]$ and $C=\left[\begin{array}{ccc}-1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2\end{array}ight]$, then $A^{-1}$ is given by

Aicharya · Accepted Answer

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

If $(B A)^{-1}=C$ where $B=\left[\begin{array}{ccc}2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & 1 & -1\end{array}\right]$…

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