Answer
$HG\text{ DOES NOT exist}$
Work Step by Step
The $row\times column$ dimension of matrix $H$ is $2\times1,$ while matrix $G$ is $2\times2$. Since the column dimension of $H$ (equal to $1$) is not equal to the row dimension of matrix $G$ (equal to $2$), then the matrix product $
HG\text{ DOES NOT exist}
.$
