I need some help proving bijections:
Suppose f is a function from $$ \mathbb R^2 \rightarrow \mathbb R^2$$
$$f(x,y) = (ax-by,bx+ay)$$
Where a,b are numbers with $$ a^2 + b^2 \neq 0 $$
Prove that f is a bijection.
I understand that a function f is a bijection if it is both an injection and a surjection so I would need to prove both of those properties.
Could you give me a hint on how to start proving injection and surjection?