#### Answer

$a_{11}=\frac{9}{5},a_{12}=6,a_{21}=\frac{−1}{5},a_{22}=−4$

#### Work Step by Step

We label the four elements of matrix $A$ using $a_{ij}$ to denote the element in the $(i,j)$th place. Then, we multiply using these elements as variables to obtain the system of equations:
$2a_{11}+3a_{21}=3
2a_{12}+3a_{22}=0
a_{11}+4a_{21}=1
a_{12}+a_{22}=2$. Solving this in the familiar way gives $a_{11}=\frac{9}{5},a_{12}=6,a_{21}=\frac{−1}{5},a_{22}=−4.$