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## Homework Statement

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

## Homework Equations

Hint was given and it was like this:

Note that [tex]x=\mathrm{T}(x)+(x-\mathrm{T}(x))[/tex] for every [tex]x[/tex] in [tex]V[/tex], and show that [tex]V=\{y:\mathrm{T}(y)=y\}\oplus\mathrm{N}(T)[/tex]

## The Attempt at a Solution

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