Let $A = \left(\begin{array}{cc} a & b \\ c & a \end{array}\right)$ be a Toeplitz matrix of size $2 \times 2$, where $(a, b, c)$ are complex numbers. Discuss, depending on the values of $(a, b, c)$, the diagonalizability of $A$.
Let $A = \left(\begin{array}{cc} a & b \\ c & a \end{array}\right)$ be a Toeplitz matrix of size $2 \times 2$, where $(a, b, c)$ are complex numbers. Discuss, depending on the values of $(a, b, c)$, the diagonalizability of $A$.