A,B is square matrices of the order n. Prove that if A and B are skew symmetric, and AB+BA = 0 then AB is also skew symmetric?
回答 (2)
2018-10-01 5:04 am
NB:--(At*Bt)=>-(A*tB*t)=>-(-A)(-B)=-AB
Being (AB)t=>-AB also.
Being (AB)t=>-AB also.
2018-10-01 4:39 am
AB + BA = 0
AB = -BA
(AB)^T = (-BA)^T = -(BA)^T
= -(A^T B^T)
A & B are skew symmetric
thus A^T = -A, B^T = -B
= -(-A)(-B) = -AB
(AB)^T = -(AB) thus AB is skew symmetric
QED
AB = -BA
(AB)^T = (-BA)^T = -(BA)^T
= -(A^T B^T)
A & B are skew symmetric
thus A^T = -A, B^T = -B
= -(-A)(-B) = -AB
(AB)^T = -(AB) thus AB is skew symmetric
QED
收錄日期: 2021-05-01 00:19:46
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