Question

证明题 设n阶方阵A满足A2-A-2I=0,求证A和（A-1)都可逆并求其逆

Answer 1

由A²-A-2E = 0, 得A(A-E) = 2E.

有A·(A-E)/2 = E, 即A可逆, A^(-1) = (A-E)/2.

A/2·(A-E) = E, 即A-E可逆, (A-E)^(-1) = A/2.