Hello,

I am stuck on the following problem:

If p is a nonnegative integer and c is a scalar, show that

$\displaystyle (cA)^p = c^p A^p$

Here is what I have started:

$\displaystyle \textrm{Let } A=[a_{ij}] \textrm{ be any } n \times n $matrix. Then

$\displaystyle (cA)^p=([ca_{ij}])^p $

Where could I go from here? Is this a good first start?