证明性质3:(A°B)T=B°AT;(4)T=(4T) 证明:设 (aim s, B=(bxnA°B=C=(少mxn 记(A°B)=(c7)nxm,4=(an7)xm,B1= in×s 由转置的定义知, C:; bT=b B°A1=IV(b∧ k川nxm =V(bk/Aa1)2×m =V(akb)1×m=(c)nxm 访质n×m (A°B)T证明性质3：( A ° B ) T = BT ° AT；( An ) T = ( AT ) n . 证明：设A=(aij)m×s , B=(bij) s×n , A °B=C =(cij)m×n , 记( A ° B ) T = (cij T ) n×m , AT = (aij T ) s×m ,BT = (bij T ) n×s , 由转置的定义知, cij T = cji , aij T = aji , bij T = bji . BT ° AT= [∨(bik T∧akj T )] n×m =[∨(bki∧ajk)] n×m =[∨(ajk∧bki)] n×m = (cji) n×m = (cij T ) n×m= ( A ° B ) T