# Find the inverse of each of the following matrices. begin{bmatrix}3 & 0 9 & 3 end{bmatrix}

Find the inverse of each of the following matrices.
$\left[\begin{array}{cc}3& 0\\ 9& 3\end{array}\right]$
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StrycharzT
Given,
$A=\left(\begin{array}{cc}3& 0\\ 9& 3\end{array}\right)$
Now determinant of A is,
$det\left(A\right)=3\left(3\right)-9\left(0\right)$
$=9-0$
$=9\ne 0$
$\therefore {A}^{-1}exists$
Step 2

$\therefore {A}^{-1}=\frac{1}{det\left(A\right)}\cdot adjA$
$=\frac{1}{9}\left(\begin{array}{cc}3& 0\\ -9& 3\end{array}\right)$
$=\left(\begin{array}{cc}\frac{1}{3}& 0\\ -1& \frac{1}{3}\end{array}\right)$
Jeffrey Jordon