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In a project I'm working on, it would be very convienent to express the inverse of this matrix in terms of its size, NxN.

The matrix is

[tex]

\leftbrace \begin{tabular}{c c c c}

a & b & \ldots & b \\

b & a & \ldots & b \\

b & b & \ddots & b \\

\vdots & vdots & ldots & b \\

b & b & \ldots & b \\

\end{tabular}

\rightbrace

[/tex]

[the tex isnt working, but the matrix is just constant b, except on the diagonal where it is a]

I can see a pattern in the inverses for N=2,3 ; the whole this is divided by det(A) and each element is given by the determinant of its corresponding cominor. This is great because it gives me a recursive formula for computing the inverse. But I'd like to be able to express it explicitly so I can write down the $$i^{th}$$ row in general

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# Inverse of a special matrix of arbitrary size

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