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矩陣請教

矩陣請教

AB皆為三階方陣,若A+B=I=100010001AB=0=000000000,則下列何者正確?
(A)B=A (B)A2=A (C)A=0B=0 (D)A2+B2=I (E)A4+B4=I

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A=AI=A(A+B)=A2+AB=A2
B=IB=(A+B)B=AB+B2=B2

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