Question
If $A=\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$ then find $A^{-1}$ by adjoint method.
✓
Answer
Given $A=\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$
$\therefore|A|=\left|\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right|=10+9=19 \neq 0$
$\therefore A ^{-1}$ exist
$A_{11}=(-1)^{1+1} \cdot M_{11}=5$
$A_{12}=(-1)^{1+2} \cdot M_{12}=-3$
$A_{21}=(-1)^{2+1} \cdot M_{21}=-(-3)=3$
$A_{22}=(-1)^{2+2} \cdot M_{22}=2$
Hence, matrix of the co-factors is
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