線代三版(上),P4-114範列1

題目:If A is m*n and B is n*m,and m>n,prove or disprove that AB is singular

ANS: rank(AB) <= rnak(A) <= n< m
因為AB為m*m矩陣 implies AB不可逆,即為singular

想請問一下為什麼AB是m*m矩陣就可以知道AB不可逆呢?