# Math Help - Help in proving (cA)^p = c^p*A^p for any matrix A

1. ## Help in proving (cA)^p = c^p*A^p for any matrix A

Hello,

I am stuck on the following problem:

If p is a nonnegative integer and c is a scalar, show that
$(cA)^p = c^p A^p$

Here is what I have started:

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

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

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

2. Originally Posted by Fourier
Hello,

I am stuck on the following problem:

If p is a nonnegative integer and c is a scalar, show that
$(cA)^p = c^p A^p$

Here is what I have started:

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

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

Where could I go from here? Is this a good first start?
Almost there!
$(cA)^p=([ca_{ij}])^p = c^p [a_{ij} ]^p = c^pA^p$

-Dan