1.letAandBbe(2×2）matrices.proveorfindacounterexampleforthisstatment:(A-B)(A+B)=A平方-B平方2.Find（2×2）matricesAandBsuchthatAandBaresymmetric,butABisnotsymmetric.是线形代数

Question

1.let A and B be(2×2）matrices.prove or find a counterexample for this statment:(A-B)(A+B)=A平方-B平方
2.Find （2×2）matrices A and B such that A and B are symmetric,but AB is not symmetric.
是线形代数

Answer 1

楼上的似乎曲解题意了……
1.Counterexample:Let A = [1 1; 0 1] B = [1 0; 1 1],then (A-B)(A+B) = [1 2; -2 -1] while A^2-B^2 = [0 2; -2 0]
2.Let A = [0 1; 1 0] B=[1 0; 0 0],then AB = [0 0; 1 0] is not symmetric