Mathematics

Problem

Let

f:A\to B

be any function between non-empty sets

A

and

B

I_A

and

I_B

denote the identity functions on

A

and

B

respectively. Which one of the following equalities holds for every such function

f

? a)

I_A\circ f = f

f\circ I_A = f

f\circ I_B = f

I_B\circ f = I_A