Question

设A,B,C均为n阶方阵,且AB=BC=CA=I,则A^2+B^2+C^2=

Answer 1

AB=BC=CA=I

AB=I => B^-1 = A

BC=I => B^-1 = C

所以 A=C

同理可得 A=B=C

所以 A^2+B^2+C^2 = AB+BC+CA = 3I