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Is there a formula for the determinant of a block matrix of this kind?

I am looking for an expression that gives the determinant of a matrix of the form \begin{bmatrix} A & B & 0 & \dots & 0 & C \\ B & A & B & & 0 & 0 \\ 0 & B & A & \ddots & 0 & \vdots \\ 0 & & & \dd …
ZingyMcGhee's user avatar