由已知,a^Ta = 1/4+1/4+1/4+1/4 = 1.
所以 AB = (I-aa^T)(I+2aa^T)
= I -aa^T + 2aa^T - aa^Taa^T
= I -aa^T + 2aa^T - a(a^Ta)a^T
= I + aa^T - aa^T
= I (单位矩阵).
由已知,a^Ta = 1/4+1/4+1/4+1/4 = 1.
所以 AB = (I-aa^T)(I+2aa^T)
= I -aa^T + 2aa^T - aa^Taa^T
= I -aa^T + 2aa^T - a(a^Ta)a^T
= I + aa^T - aa^T
= I (单位矩阵).