$A=\left[\begin{array}{lll}0 & 1 & 2 \ 1 & 2 & 3 \ 3 & a & 1\end{array} ight]$ and $A^{-1}=\frac{1}{2}\left[\begin{array}{ccc}1 & -1 & 1 \ -8 & 6 & 2 c \ 5 & -3 & 1\end{array} ight]$, then values of $a$ and $\mathrm{c}$ are respectively

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$A=\left[\begin{array}{lll}0 & 1 & 2 \ 1 & 2 & 3 \ 3 & a & 1\end{array}ight]$ and $A^{-1}=\frac{1}{2}\left[\begin{array}{ccc}1 & -1 & 1 \ -8 & 6 & 2 c \ 5 & -3 & 1\end{array}ight]$, then values of $a$ and $\mathrm{c}$ are respectively

Aicharya · Accepted Answer

We know that $\mathrm{AA}^{-1}=1$ $\begin{aligned} & 	herefore\left[\begin{array}{lll} 0 & 1 & 2 \ 1 & 2 & 3 \ 3 & \mathrm{a} & 1 \end{array}ight]\left[\begin{array}{ccc} \frac{1}{2} & \frac{-1}{2} & \frac{1}{2} \ -4 & 3 & \mathrm{c} \ \frac{5}{2} & \frac{-3}{2} & \frac{1}{2} \end{array}ight]=\left[\begin{array}{ccc} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}ight] \ & 	herefore\left[\begin{array}{ccc} 1 & 0 & \mathrm{c}+1 \ 0 & 1 & 2+2 \mathrm{c} \ 4-4 \mathrm{a} & 3 \mathrm{a}-3 & 2+\mathrm{ac} \end{array}ight]=\left[\begin{array}{ccc} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{array}ight] \end{aligned}$ Thus $\mathrm{c}+1 \Rightarrow \mathrm{c}=-1$ and $4-4 \mathrm{a}=0 \Rightarrow \mathrm{a}=1$

$A=\left[\begin{array}{lll}0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & a & 1\end{array}\right]$ and…

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