Show that if a^3 = b^3 if and only if a=b

Suppose a = b

a^3 = (a)(a)(a)

=(b)(b)(b)

=b^3

Prove other direction using contrapositive:

Suppose a != b, then a^3 != b^3

Case 1:

a>b

****I'm a little stuck here, I'm not sure if I'm allowed to say aaa>bbb by assuming a>b

a^3 = (a)(a)(a)

>(b)(b)(b)

=b^3

a^3 != b^3