CIIM 2011 Problem 4

For $n \geq 3$ , let $(b_0, b_1,..., b_{n-1}) = (1, 1, 1, 0, ..., 0).$ Let $C_n = (c_{i, j})$ the $n \times n$ matrix defined by $c_{i, j} = b _{(j -i) \mod n}$ . Show that $\det (C_n) = 3$ if $n$ is not a multiple of 3 and $\det (C_n) = 0$ if $n$ is a multiple of 3.