| a b ⋯ b b a ⋯ b ⋮ ⋮ ⋱ ⋮ b b ⋯ a | = | 1 b b ⋯ b 0 a b ⋯ b 0 b a ⋯ b ⋮ ⋮ ⋮ ⋱ ⋮ 0 b b ⋯ a | = | 1 b b ⋯ b − 1 a − b 0 ⋯ 0 − 1 0 a − b ⋯ 0 ⋮ ⋮ ⋮ ⋱ ⋮ − 1 0 0 ⋯ a − b | {\displaystyle {\begin{vmatrix}a&b&\cdots &b\\b&a&\cdots &b\\\vdots &\vdots &\ddots &\vdots \\b&b&\cdots &a\end{vmatrix}}={\begin{vmatrix}1&b&b&\cdots &b\\0&a&b&\cdots &b\\0&b&a&\cdots &b\\\vdots &\vdots &\vdots &\ddots &\vdots \\0&b&b&\cdots &a\end{vmatrix}}={\begin{vmatrix}1&b&b&\cdots &b\\-1&a-b&0&\cdots &0\\-1&0&a-b&\cdots &0\\\vdots &\vdots &\vdots &\ddots &\vdots \\-1&0&0&\cdots &a-b\end{vmatrix}}}