Consider A, B and C, all nxn matrices. Show that: 1) det(A)=det(A^T) 2) if C was...

Consider A, B and C, all nxn matrices.
Show that:
1) det(A)=det(A^T)
2) if C was obtained from A by changing the i-th row (column) with the j-th row (column). Show that det(C)=-det(A)
3) det(AB)=det(A)det(B)
4) Let C be a matrix obtained from A by multiplying a row by c ∈ F. Show that det(B)=c · det(A)

Expert Solution

Colby Messinger answered 2 years ago

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Question

Consider A, B and C, all nxn matrices. Show that: 1) det(A)=det(A^T) 2) if C was...

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