We consider the matrix $$A = A(\mu) = \left(\begin{array}{ccc} 2-\mu & -1 & \mu \\ -1 & 2-\mu & \mu-1 \\ 0 & -1 & 1 \end{array}\right)$$ Show that $A(\mu)$ is invertible for every real $\mu$.
We consider the matrix
$$A = A(\mu) = \left(\begin{array}{ccc} 2-\mu & -1 & \mu \\ -1 & 2-\mu & \mu-1 \\ 0 & -1 & 1 \end{array}\right)$$
Show that $A(\mu)$ is invertible for every real $\mu$.