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標題:

al matrix with inequality

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發問:

Let A be a 3x3 matrix with property that A^2=O or A^2=I,where O and I are the 3x3 zero matrix and 3X3 identity matrix, respectively. Prove that det(A+I)>=det(A-I)

最佳解答:

If AA = I 0 0 Now as (– A) (– A) = AA = I or O, det [I + (– A)] => 0 Then det(A – I) = - det (I – A) = - det [I + (– A)] 0 => det(A – I) 2010-05-08 22:36:41 補充： 小錯誤 det(2A+2I) = det(2 I) det (A+I) = 8 det(A + I) for 3x3 matrix

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