Question

试证：如A是n阶方阵满足A*A=E,则秩（A+E）+秩（A-E）=n

Answer 1

由A^2 = E 得 (A+E)(A-E) = 0

所以 r(A+E) + r(A-E) = r (A+E + E-A) = r(2E) = r(E) = n

所以 r(A+E) + r(A-E) = n.

满意请采纳^_^