what is the direct method of finding nth power value of matrix say A is 2x2 matrix with say 2 2 3 4 values...now i want [A] ^n

Question

we can find the same with diagonalisation but its too lenghty process. I would like to know the shortcut

i tried diagonalisation method in which we find the eigen values and then find the modal matrix and then fill the matrix with those values. After that we can square the matrix it can give nth time of given matrix. But this process is time consuming