I have an undefined 2x2 matrix with trace = 2 and determinant = 12. I need to figure out if it's diagonalizable, and if it can be symmetric, and orthogonal.
I've determined that its eigenvalues are 2 & 6 using:
$\lambda_{\pm}=\frac{1}{2}(8\pm\sqrt{8^2-4(12)})=2,6$
And that therefor it is diagonizable since each eigenvalue's multiplicity is 1. However, I am unsure of how to find if it can be symmetric and orthogonal. I can't seem to find properties that would allow me to discern this. Is there a way to approach this given the information I have?