Show that all irreducible representations of a finite group are finite dimensional.

Show that all irreducible representations of a finite group are finite dimensional.
We know for any representation $V$ of a finite group $G$, there is a decomposition $V=V_1 \oplus V_2 \oplus.....\oplus V_n$ where $V_i$ s are all irreducibles. Now if we make $V$ irreducibles then just one $V=V_1$(say) will be there. But how can we show $V$ is finite dimensional?

Any help will be apreciated..

Answer

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Source : Link , Question Author : Ri-Li , Answer Author : whacka