I've been going through properties of determinants of matrices and found the following:(adsbygoogle = window.adsbygoogle || []).push({});

Assuming products are defined and the matrices involved are nonsingular of the same order

The determinant of the product of any number of matrices is equal to the determinant of each matrix; where the order of factors does not matter

det(AB)=det(A)det(B)

det(AB)=det(B)det(A)

det(BA)=det(A)det(B)

det(BA)=det(B)det(A)

det(ABC)=det(C)det(A)det(B)

det(ACB)=det(A)det(B)det(C)

Is this correct? And is there a way to describe this property regarding commutatively? I know in general matrix multiplication is not commutative unless the matrices involved are diagonal and of the same dimension. However the determinant operator seems to not preserve the non commutative property of matrix multiplication, on either side of the equality. What I’m looking for here is a formal way of describing this property that encompasses the fact that order of factors does not matter and if commutativity should be used in any part of this description.

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# Matrix determinant operator commutative?

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