det. walter beckwith

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? linear algebra - How to show that $\det (AB) =\det (A) \det (B ... 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 It would be a good exercise to determine for which matrices, the identity $\det (A+b)=\det (A)+\det (B)$ holds. I think that it would work for rather few of them.

Prove $$\\det \\left( e^A \\right) = e^{\\operatorname{tr}(A)}$$ for all matrices $A \\in \\mathbb{C}^{n \\times n}$. linear algebra - How to prove $\det \left (e^A\right) = e ...