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?