\left(\begin{array}{cc}
2 & 3 \\
3 & -2
\end{array}\right)\left(\begin{array}{l}
a \\
b
\end{array}\right)=\left(\begin{array}{l}
5 \\
1
\end{array}\right)
then,
\begin{array}{l}
2 a+3 b=5 \ldots \ldots . . \text { (i) } \\
3 a-2 b=1 \ldots \ldots . . . \text { (ii) }
\end{array}
Multiply equation (i) by 2 and equation (ii) by 3 \(2(2 \mathrm{a}+3 \mathrm{~b})=5 \times 2 4 \mathrm{a}+6 \mathrm{~b}=10 \ldots\) (iii)
\(3(3 a-2 b)=1 \times 3\)
\(9 a-6 b=3 \ldots \ldots \ldots . .(\) iv \()\)
add equations (iii) \& (iv)
\(13 a=13, a=13 / 13=1\)
put \(a=1\) into equation (i)
\(2(1)+3 b=5\)
\(2+3 b=5\)
\(3 b=5-2=3, b=3 / 3=1\)