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
Let $A$ be an $n \times n$ matrix and $k$ be a scalar. Prove that $\det(kA)=k^n\det A$. I really don't know where to start. Can someone give me a hint for this proof?
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 ...
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.
linear algebra - Does $\det (A + B) = \det (A) + \det (B)$ hold ...
In this case, obviously, $\det (A)=\det (A^*)$, but this is not generally true. You can decompose taking the conjugate transpose in two steps: first conjugate each entry, then transpose.
linear algebra - Describe $\det (A^*)$ in terms of $\det (A ...
Professor Mikael B. Skov er udpeget som prodekan for forskning på TECH på Aalborg Universitet. Han kommer fra en stilling som professor på Institut for Datalogi, hvor han leder forskningsgruppen Human ...