The condition number of a rectangular matrix inCmn is defined as (A)=AA, whereA denote the Moore-Penrose inverse of A. Here denotes a submultiplicative matrix norm. Show that for any nonzero matrix ACmn, (A)1.

(I've tried using SVD which leads to (A)UU, but then I'm stuck. It is only given that the norm is submultiplicative. Even if(A)UUI somehow, I think it is not necessary thatI=1 .)

(thank you in advance for your help!)