Answer
The inverse does not exist.
Work Step by Step
Let $A= \begin{bmatrix} 4 & 12 \\ 2 & 6 \end{bmatrix}$, do row operations, we have :
$AI= \begin{bmatrix} 4 & 12 \\ 2 & 6 \end{bmatrix}\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}\begin{array} .\\2R2-R1\to R2\\ \end{array}$
$ \begin{bmatrix} 4 & 12 \\ 0 & 0 \end{bmatrix}\begin{bmatrix} 1 & 0 \\ -1 & 2 \end{bmatrix}\begin{array} .\\2R2-R1\to R2\\ \end{array}$
As we can not obtain an identity matrix on the left with a row of zeros, the inverse does not exist.
