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### Why is the determinant of the all one matrix minus the identity matrix n-1? [duplicate]

Context (skippable) I was asked (by a friend who is preparing for an exam) whether there was a special trick to compute the determinant of the following matrix. I didn't see anything beyond using the ...
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### Calculate $\lvert A \rvert$ if $a_{ij}=0$ if $i=j$ and $1$ otherwise [duplicate]

Let $n$ be a positive integer and let $A=[a_{ij}] \in M_{n\times n} (R)$ be the matrix defined by $a_{ij}=0$ if $i=j$ $1$ otherwise To be honest, I've only calculated determinants of matrices ...
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### What is the determinant value of $J-I$ if $I$ is identity matrix and $J=(1)_{101\times 101}$? [duplicate]

Let $J$ be a matrix of order $101\times 101$ which each entry is 1 and suppose $I_{101}$ is identity matrix of order $101\times 101$. The question is : what should be the determinant value of $J-I$ ? ...
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### Diagonal entries are zero, others are $1$. Find the determinant. [duplicate]

$\det\begin{vmatrix} 0 & \cdots & 1& 1 & 1 \\ \vdots & \ddots & \vdots & \vdots & \vdots \\ 1 & \cdots & 1 & 1 & 0 \end{vmatrix}=?$ Attempt: First I ...
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### determinant of an $n\times n$ matrix type [duplicate]

Possible Duplicate: How to calculate the following determinants Computing determinant of a specific matrix. How can one compute the determinant of an $n\times n$ matrix where all the diagonal ...
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### Proof explanation about the computation of a certain determinant by Sylvester's theorem [duplicate]

Let $n\geq 2$, $A=[a_{ij}]\in Mat_n(\mathbb{R})$ the matrix defined by $a_{ij}=0$ if $i=j$ and $a_{ij}=1$ if $i\not =j$ Calculate $\det(A)$ Proof: Sylvester's theorem: https://en.wikipedia.org/...
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### Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
This question aims to create an "abstract duplicate" of numerous questions that ask about determinants of specific matrices (I may have missed a few): Eigenvalues of a matrix of $1$'s ...