Prove that for any matrix A and any vector norm ||·|| the following definitions of subordinate matrix norm ||A|| are equivalent...

||A|| = max(x!=0) ||Ax||/||x||

and

||A|| = max(||u||=1) ||Au||

I know I probably have to use the definitions of a matrix norm but I'm stumped. I don't really understand the topic all that well and none of the information I've found is very helpful.

Once again, any help greatly appreciated and sorry about the rubbish formatting.