Find the inverse of each of the matrices (if it exists).
Question:

Find the inverse of each of the matrices (if it exists).

$\left[\begin{array}{rr}2 & -2 \\ 4 & 3\end{array}\right]$

Solution:

Let $A=\left[\begin{array}{rr}2 & -2 \\ 4 & 3\end{array}\right]$.

we have.

$|A|=6+8=14$

Now,

$A_{11}=3, A_{12}=-4, A_{21}=2, A_{22}=2$

$\therefore \operatorname{adj} A=\left[\begin{array}{ll}3 & 2 \\ -4 & 2\end{array}\right]$

$\therefore A^{-1}=\frac{1}{|A|}$ adjA $=\frac{1}{14}\left[\begin{array}{ll}3 & 2 \\ -4 & 2\end{array}\right]$

 

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