If `f: A->A ,\ \ g: A->A` are two bijections, then prove that `fog` is an injection.

Explanation

Let `a, b in A`.


Now,


`(f circ g)(a)=(f circ g)(b)`


or, `{f}[{g}({a})]={f}[{g}({b})][` Since `{g}` is bijective this gives `{g}` is surjective then `{g}({a}), {g}({b}) in {A}]`


or, `g(a)=g(b)` [ Since `f` is bijective this gives `f` is one-one also]


or, `{a}={b}` [ Since `{g}` is one-one `]`


This gives `f circ g` is one-one or injection.