characteristic equation is
(a-$\lambda$)[(d-$\lambda$)*(-$\lambda$)+1]-b[-c$\lambda$-1]+1[-c-d+$\lambda$]=0
(a-$\lambda$)[-d$\lambda$+$\lambda^{2}$+1]+bc$\lambda$+b-c-d+$\lambda$=0
-ad$\lambda$+a$\lambda^{2}$+a+d$\lambda^{2}$-$\lambda^{3}$-$\lambda$+bc$\lambda$+b-c-d+$\lambda$=0
-$\lambda^{3}$+(a+d)$\lambda^{2}$+(-ad-1+bc+1)$\lambda$+(a+b-c-d)=0
$\lambda^{3}$-(a+d)$\lambda^{2}$+(bc-ad)$\lambda$=0 (a+c=c+d)
$\lambda$=0 or
$\lambda^{2}$-(a+d)$\lambda$+(bc-ad)=0
$\lambda$=$\frac{(a+d)\pm \sqrt{(a+d)^{2}-4*(1)*(bc-ad)}}{2}$
$\lambda$=$\frac{(a+d)\pm \sqrt{a^{2}+2ad+d^{2}-4bc+4ad}}{2}$
$\lambda$=$\frac{(a-d)\pm \sqrt{(a-d)^{2}+4bc}}{2}$
$\lambda$=$\frac{(a-d)\pm \sqrt{(c-b )^{2}+4bc}}{2}$ (a+b=c+d)
$\lambda$=$\frac{(a+d)\pm (b+c)}{2}$
$\lambda$= a+b or $\lambda$=c+d
