Inverse of a 2×2 matrix

A={{a,b},{c,d}};
MatrixForm[A]

Inverse[A]//MatrixForm

Inverse of a 3×3 matrix

A={{a,b,c},{d,e,f},{g,h,i}};
MatrixForm[A]

Inverse[A]//MatrixForm

Inverse of a 4×4 matrix

A={{a,b,c,d},{e,f,g,h},{i,j,k,l},{m,n,o,p}};
MatrixForm[A]

Inverse[A]//MatrixForm

Check the determinant we computed by hand

A={{9,2,3,2},{2,0,2,5},{0,3,0,0},{3,1,0,-1}}
Det[A]