Solve A^2*Y*B^-1=A

$$A ^ { 2 } \cdot Y \cdot B ^ { - 1 } = A$$

Solve for B

$$\left\{\begin{matrix}B=AY\text{, }&Y\neq 0\text{ and }A\neq 0\\B\neq 0\text{, }&A=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Reorder the terms.

$$\frac{1}{B}YA^{2}=A$$

Variable B cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by B.

$$1YA^{2}=AB$$

Swap sides so that all variable terms are on the left hand side.

$$AB=1YA^{2}$$

Reorder the terms.

$$AB=YA^{2}$$

Divide both sides by A.

$$\frac{AB}{A}=\frac{YA^{2}}{A}$$

Dividing by A undoes the multiplication by A.

$$B=\frac{YA^{2}}{A}$$

Divide A^{2}Y by A.

$$B=AY$$

Variable B cannot be equal to 0.

$$B=AY\text{, }B\neq 0$$

Solve for A

$$\left\{\begin{matrix}A=0\text{, }&B\neq 0\\A=\frac{B}{Y}\text{, }&Y\neq 0\text{ and }B\neq 0\end{matrix}\right.$$