Matrix Multiplication Properties for 2x2 Matrices

[nokia8650]

Where A = a 2*2 matrix, is the following true:

(A^n)(A^m) = (A^m)(A^n)

Thanks in advance

 

[Dick]

Take a guess. Tell us why it might be true.

 

[nokia8650]

Well I think it would be true, however I know that matrix multiplication is non-commutative so I wasnt sure.

Thanks

 

[Dick]

Matrix multiplication isn't commutative in general. But this is special. It IS associative. Both sides of that equation have n+m A's. They are just grouped differently.