Finding the eigenvalues of $\begin{pmatrix} a & b \\ b & a \end{pmatrix}$ matrix without the determinant
Hint:
You are so close: simplifying by $x$,
$$\frac{\lambda -a}b=\frac b{\lambda -a}$$ can be solved for $\lambda$.
Hint:
You are so close: simplifying by $x$,
$$\frac{\lambda -a}b=\frac b{\lambda -a}$$ can be solved for $\lambda$.