Re: [線代] AB=O
※ 引述《mqazz1 (無法顯示)》之銘言：
: Let A, B denote two n*n matrices satisfying AB=O.
: Then in the following, pick up the correct statements.
: (a) BA=O
False,
let A=[ 1 0 ] B=[ 0 0 ]
[ 0 0 ] [ 1 0 ]
then AB = 0, but BA != 0
: (b) all eigenvalues of BA are 0
: (c) (BA)^2 = O
True,
(BA)^2 = BABA = B(AB)A = 0
: (d) A=O or B=O
False, Similary to (a)
: (e) rank(A) + rank(B) = n
False,
pick A=B=0
: 謝謝
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