線性代數習題7-9(T or F)

Let T be a linear operator on V. If||T(x)||=||x||,then T is onto.

本題的上一題是問one-to-one 很好證(即證Ker(T)={0})

那為什麼one-to-one 加上||T(x)||=||x|| 就可得T為 onto 呢