I need to prove that |adj(A)|=|A|^(n-1) for every non singular A in F^nxn, while n>2.

The solution says:

http://img190.imageshack.us/img190/1217/43950593.png

I can understand the first equality - |adj(A)|=||A|*A^(-1)|,

but I can't understand the rest.

Can you please help me?

Thank you! :)