R-Squared Invariance Under Transformations

Consider the simple linear regression $Y = \alpha + \beta X + \epsilon$. (a) If you multiply all $X$ values by a constant $c \neq 0$, what happens to $R^2$? (b) If you add a constant $k$ to all $Y$ values, what happens to $R^2$? (c) If you add a new predictor $Z$ that is perfectly collinear with $X$ (i.e., $Z = aX + b$ for constants $a, b$), can $R^2$ increase?