Matrix and Determinant
2012-03-05 2:10 am
For a 3 x 3 square matrix A, prove that A^2 = A only if A = I or A is singular. (If not true, please give an example).
回答 (2)
2012-03-05 4:06 am
✔ 最佳答案
Solution:det(A^2) = det(A)
det(A) = 0 or 1
If det(A) = 0, A is singular.
If det(A) = 1, it has inverse A^(-1). So,
A^2 = A => A = I
This proves that A^2 = A only if A = I or A is singular.
收錄日期: 2021-04-26 19:17:46
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