# Squaring a linear transformation

## Homework Statement

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!

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Ray Vickson
Homework Helper
Dearly Missed

## Homework Statement

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

RGV

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

RGV
Thank you! I should have guessed that.