## Determine the Values of $a$ such that the 2 by 2 Matrix is Diagonalizable

## Problem 459

Let

\[A=\begin{bmatrix}

1-a & a\\

-a& 1+a

\end{bmatrix}\]
be a $2\times 2$ matrix, where $a$ is a complex number.

Determine the values of $a$ such that the matrix $A$ is diagonalizable.

(*Nagoya University, Linear Algebra Exam Problem*)