For Eigen Values:
Let us suppose eigenvalues are $\lambda_{1},\lambda_{2}$
Sum of all Eigen Values$= $Trace of the matrix=Sum of Leading diagonal element
$\lambda_{1}+\lambda_{2}=0$------->(1)
Product of all diagonal element$=Det(A)=|A|$
$\lambda_{1}.\lambda_{2}=-9-16$
$\lambda_{1}.\lambda_{2}=-25$------>(2)
Now ,we can make Quadratic Equation if given roots are $\lambda_{1},\lambda_{2}$
$x^{2}-(\lambda_{1}+\lambda_{2})x+\lambda_{1}.\lambda_{2}=0$
put the value from the abpve equation $(1)$ and $(2)$,and we get
$x^{2}-0.x-25=0$
$x^{2}-25=0$
$x^{2}=25$
$x=5,-5$
So$,\lambda_{1}=-5,\lambda_{2}=5$