Property of matrix determinant--am I correct?

Factual Questions
1

Suppose A and B are two nxn (i.e., square) matrices and let det(.) be the determinant function. Is the following statement correct?

det(AB) = det(BA)

?

I know such a commutative relationship holds for the trace, and for some reason I thought it held for determinants as well, but I can’t find it listed among the properties of determinants in my textbook or on the Wikipedia article.

Thanks in advance for your help :slight_smile:

2

From my Linear Algebra book

If A and B are n x n matricies, then det(AB) = det(A) • det(B)

I would gather from that that det(AB) = det(BA) since the commutative property should hold for the right side of the above equation.

3

Ah, of course! That product rule was what I was missing. Thanks much!