矩陣請教
設\(A\)、\(B\)皆為三階方陣，若\(A+B=I=\left[\matrix{1&0&0\cr 0&1&0\cr 0&0&1} \right]\)，\(AB=0=\left[\matrix{0&0&0\cr 0&0&0\cr 0&0&0} \right]\)，則下列何者正確？(A)\(B=-A\) (B)\(A^2=A\) (C)\(A=0\)或\(B=0\) (D)\(A^2+B^2=I\) (E)\(A^4+B^4=I\) \(A = AI = A(A + B) = A^2 + AB = A^2\)
\(B = IB = (A + B)B = AB + B^2 = B^2\)
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