# Squaring a linear transformation

1. Oct 28, 2011

### starcoast

1. The problem statement, all variables and given/known data
Prove that T$^{2}$ is a linear transformation if T is linear (from R$^{3}$ to R$^{3}$.

So I understand when a transformation is considered linear, but I don't understand what squaring a transformation does. I don't think it means squaring the result of the transformation but I'm not sure how else to think of it. Or maybe I'm forgetting some convenient property that would make this proof short and sweet. Any help is very much appreciated!

2. Oct 28, 2011

### Ray Vickson

T^2(x) = T(T(x)).

RGV

3. Oct 28, 2011

### starcoast

Thank you! I should have guessed that.