例6：设A,B均为n阶方阵 且A4=E,BB=E, =-1, B 则A+B=O. 证A+B-ABTB+AMTB =A(BT+AT)B =(4+B)TB =-B4+B =-4+B 故A+B 例6：设A , B 均为 n 阶方阵 且 , , 1, T T = = = − B A AA E B B E 则A+ B = 0. 证 A B AB B AA B T T + ＝ + A(B A )B T T = + A A B B T = ( + ) = − B A+ B 2 = − A+ B 故 A+ B = 0