Direct sums and idempotent transformations

Let $T : V \to V$ be a linear transformation on a finite-dimensional vector space. Prove that if $T^{2} = T$ , then

V = \ker (T) \oplus im (T) .

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Let $T:V\to V$ be a linear transformation on a finite-dimensional vector space. Prove that if $T^2=T$, then
\[
	V=\ker(T)\oplus \operatorname{im}(T).
\]