Given that :
1) det A = - 1.
2) det (A - I) = 0.
3) det (A + I) = 0.
Prove that (A + I)(A - I)^2 = (A - I)^2(A + I) = (A - I)(A + I)(A - I) = 0 ( zero matrix, not simply singular matrix).
更新1:
To : ：自由自在 By the same token, if x^n = (x - 1)^(x + 1)g(x) + px^2 + qx + r, can we say that this is the characteristic polynomial for matrix A, if A satisfies all 3 conditions. That is A^n = (A - I)^2(A + I) g(A) + pA^2 + qA + rI ?
