I've a math problem that I can't solve which is:

How do I prove that if a function is bijective then it's inverse is also bijective?

I know I've to prove that if

then

So then the inverse is injective.

Then to prove a function

is surjective I've to show that each element of

is the image of at least one element of

If I can show these two to be valid then the inverse is bijective.

Can anyone kindly tell me how do I show this?

How do I show that a inverse of a bijective function is injective and surjective?