Given two square matrices $A$ and $B$, how do you show that $$\det (AB) = \det (A) \det (B)$$ where $\det (\cdot)$ is the determinant of the matrix?
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11 I believe your proof is correct. Note that the best way of proving that $\det (A)=\det (A^t)$ depends very much on the definition of the determinant you are using. My personal favorite way of proving it is by giving a definition of the determinant such that $\det (A)=\det (A^t)$ is obviously true.
How do I prove that $\det A= \det A^T$? - Mathematics Stack Exchange
linear algebra - How to show that $\det (AB) =\det (A) \det (B ...
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