[理工] 線性代數

[B90165 (abc)]

If an nxn matrix A, which has the property of A = -AT; prove that

detA = (-1)^n detA.


Prove that (AB)T = BT*AT, where A and B are matrices, and T represents the
transpose operations


這2題要怎證明

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推 squallting:記得第二題板上不久前才有人問過
推 kuso0516:det(A)=det(-AT)=(-1)^n * det(AT)=(-1)^n * det(A)
推 AIdrifter:看到熟人推一下XD
推 loveray78327:det((AB)T)=det(AB)=det(A)det(B)=det(B)det(A)
→ loveray78327:=det((B)T)det((A)T)=det((B)T(A)T) =>(AB)T =ATBT