Matrix Exponentiation

Which best describes the time to compute A^m where A is an n x n matrix and m is an integer > 2 combining the traditional algorithm for the product of two matrices but using "binary decomposition" decrease-and-conquer to compute exponentiation for higher powers?

A) (n^2 x m)

B) (m^2 x n)

C) (n^2 log m)

D) (m^2 log n)

E) (n^3 x m)

F) (m^3 x n)

G) (n^3 log m)

H) (m^3 log n)

I) (n^4)

J) (m^4)

Please, include explanation with your answer.