Inverse of a Matrix

Consider the $ n $x$ n $ matrix $ A $. The inverse of $ A $ is defined as $ A^{-1} $ such that $ AA^{-1} = A^{-1}A=I_n $ where $ I_n $ is the identity matrix.

For example let

$ A= \begin{bmatrix} 1 & 4 \\ 1 & 3 \end{bmatrix} $

Then the inverse of A is

$ A^{-1} = \begin{bmatrix} -3 & 4 \\ 1 & -1 \end{bmatrix} $