# Three diagonal matrix inverse condition [duplicate]

Let $a$ is a constant. For which condition(s) this matrix has an inverse?
$$\left[ \begin{array}{cccccc} a & 1 & 0 & \cdots & & 0 \\ 1 & a & 1 & \cdots & & 0 \\ 0 & 1 & \ddots & & & \\ \vdots & \vdots & & a & 1 & 0 \\ & & & 1 & a & 1 \\ 0 & 0 & \cdots & 0 & 1 & a \\ \end{array} \right]$$
• Any thoughts of your own? Did you try solving it for the $2\times 2$ and $3\times 3$ cases? – Casteels Jun 16 '15 at 12:09