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**arze** Let **A** be the matrix $\displaystyle \left(\begin{array}{cc}a&b\\c&d\end{array}\right)$, where no one of *a,b,c,d* is zero. It is required to find a non-zero 2x2 matrix **X** such that **AX+XA=0**, where **0** is the zero 2x2 matrix. Prove that either

(a) *a+d=0*, in which case the general solution for **X** depends on two parameters, or

(b) *ad-bc=0,* in which case the general solution for **X** depends on one parameter.

I don't know where to begin other than naming **X**=$\displaystyle \left(\begin{array}{cc}\\x_{11}&x_{12}\\x_{21}&x_{ 22}\end{array}\right)$ and then find the matrices **AX** and **XA**.

Thanks