LetAbe the matrix , where no one ofa,b,c,dis zero. It is required to find a non-zero 2x2 matrixXsuch thatAX+XA=0, where0is the zero 2x2 matrix. Prove that either

(a)a+d=0, in which case the general solution forXdepends on two parameters, or

(b)ad-bc=0,in which case the general solution forXdepends on one parameter.

I don't know where to begin other than namingX= and then find the matricesAXandXA.

Thanks