## Homework Statement

Let $$\mathrm{V}$$ be a vector space. Determine all linear transformations $$\mathrm{T}:V\rightarrow V$$ such that $$\mathrm{T}=\mathrm{T}^2$$.

## Homework Equations

Hint was given and it was like this:
Note that $$x=\mathrm{T}(x)+(x-\mathrm{T}(x))$$ for every $$x$$ in $$V$$, and show that $$V=\{y:\mathrm{T}(y)=y\}\oplus\mathrm{N}(T)$$

## The Attempt at a Solution

I tried to calculate $$T(x)$$ and $$T^2(x)$$ using $$x=T(x)+(x-T(x))$$ and put $$T$$ and $$T^2$$ equal. But, I do not think this is how to solve this problem... =(

## Answers and Replies

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