A square matrix is called a permutation matrix if it contains the entry $1$ exactly once in each row and in each column, with all other entries being $0$. All permutation matrices are invertible. Find the inverse of the permutation matrix $$A = \left[\begin{array}{cccc} 0 &0 &1 &0\cr 1 &0 &0 &0\cr 0 &0 &0 &1\cr 0 &1 &0 &0 \end{array}\right].$$