Question
If $A=\left[\begin{array}{cc}5 & 4 \\ -2 & 3\end{array}\right]$ and $\left[\begin{array}{cc}-1 & 3 \\ 4 & -1\end{array}\right]$ then find $C^{\top}$, such that $3 A-2 B+C=I$, where $I$ is the
unit matrix of order 2.
unit matrix of order 2.
$\begin{aligned} \therefore \quad C & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]+2\left[\begin{array}{cc}-1 & 3 \\ 4 & -1\end{array}\right]-3\left[\begin{array}{cc}5 & 4 \\ -2 & 3\end{array}\right] \\ & =\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]+\left[\begin{array}{cc}-2 & 6 \\ 8 & -2\end{array}\right]-\left[\begin{array}{cc}15 & 12 \\ -6 & 9\end{array}\right] \\ & =\left[\begin{array}{cc}1-2-15 & 0+6-12 \\ 0+8+6 & 1-2-9\end{array}\right]\end{aligned}$
$\begin{array}{ll}\therefore & C=\left[\begin{array}{cc}-16 & -6 \\ 14 & -10\end{array}\right] \\ \therefore & C^{\mathrm{T}}=\left[\begin{array}{cc}-16 & 14 \\ -6 & -10\end{array}\right]\end{array}$
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