Prove that the regression R2 is identical to the square of the correlation

Prove that the regression R2 is identical to the square of the correlation coefficient between two variables Y and X.

Regression functions are written in a form that suggests causation running from X to Y. Given your proof, does a high regression R2 present supportive evidence of a causal relationship? Can you think of some regression examples where the direction of causality is not clear? Is without a doubt?