How to find characteric polynomial of a 2x2 matrix?

The roots of the characteristic equation are the eigenvalues. Suppose they are a and b, then the characteristic equation is (x−a)(x−b)=0⟹x2−(a+b)x+ab=0. The product of eigenvalues is the determinant, and the sum is the trace, hence weget the equation x2−tr(A)x+det(A)=0.

Cwill be your correct answer