Solve PA+PB=2I

$$P A + P B = 2 I$$

Solve for A

$$\left\{\begin{matrix}A=-B+\frac{2I}{P}\text{, }&P\neq 0\\A\in \mathrm{R}\text{, }&I=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract PB from both sides.

$$PA=2I-PB$$

The equation is in standard form.

$$PA=2I-BP$$

Divide both sides by P.

$$\frac{PA}{P}=\frac{2I-BP}{P}$$

Dividing by P undoes the multiplication by P.

$$A=\frac{2I-BP}{P}$$

Divide 2I-PB by P.

$$A=-B+\frac{2I}{P}$$

Solve for B

$$\left\{\begin{matrix}B=-A+\frac{2I}{P}\text{, }&P\neq 0\\B\in \mathrm{R}\text{, }&I=0\text{ and }P=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract PA from both sides.

$$PB=2I-PA$$

The equation is in standard form.

$$PB=2I-AP$$

Divide both sides by P.

$$\frac{PB}{P}=\frac{2I-AP}{P}$$

Dividing by P undoes the multiplication by P.

$$B=\frac{2I-AP}{P}$$

Divide 2I-PA by P.

$$B=-A+\frac{2I}{P}$$