# Questions tagged [determinant]

Questions about determinants: their computation or their theory. If $E$ is a vector space of dimension $d$, then we can compute the determinant of a $d$-uple $(v_1,\ldots,v_d)$ with respect to a basis.

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### Finding the determinant of a $3*3$ matrix that was developed using LaGrangian multiplier to optimize the surface area of a conical frustum

This is the matrix I wrote down. I'm struggling to find its determinant as by hand it would be impractical and would take a lot of time, is there any online calculator or a way to find it quickly, if ...
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### How many different determinants are possible by reordering entries?

I was preparing a worksheet about cofactor expansion of $3\times3$ determinants and decided to create only matrices of order 3 whose entries are among $\pm1,\pm2,\dots,\pm9$ such that the absolute ...
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### Does $\det(AB) = \det(A) \det(B)$ hold for differential operators $A$ and $B$?

Following the inconsistency I was facing in a previous post, I was wondering if the following property $$\det(A) \det(B) = \det(AB)$$ holds for generic $A$ and $B$ differential operators. It looks ...
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### Solving a matrix equation involving trace and determinant

Let $n\in\mathbb{Z}_{>1}$. Consider the following set : $$E_n=\{A\in\mathcal{M}_n(\mathbb{C})| \mathrm{Tr}(A)=\det(A)\}$$ My goal is to characterize $E_n$ for any $n$. I have already found a ...
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