Matrix

2011-11-01 5:56 am
A is a 2 x 2 matrix with det A = - 1.
If det(A + I) = det(A - I) = 0, is it always true that A^2 = I. If not, please give an example of A.
更新1:

To : 自由自在 Thanks for the proof. Is this also true for 3 x 3 matrix ? Seems not. What is your opinion?

回答 (1)

2011-11-01 6:26 am
✔ 最佳答案
http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-126.jpg

圖片參考:http://i1090.photobucket.com/albums/i376/Nelson_Yu/int-126.jpg


2011-11-01 20:24:59 補充:
Not true for 3x3. For example, A = (1,1,1)(0,1,1)(0,0,-1)


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