Solve A*x-B=I

$$A \cdot x - B = I$$

Solve for A (complex solution)

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

Steps for Solving Linear Equation

Add B to both sides.

$$Ax=I+B$$

The equation is in standard form.

$$xA=B+I$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{B+I}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{B+I}{x}$$

Solve for A

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

Steps for Solving Linear Equation

Add B to both sides.

$$Ax=I+B$$

The equation is in standard form.

$$xA=B+I$$

Divide both sides by x.

$$\frac{xA}{x}=\frac{B+I}{x}$$

Dividing by x undoes the multiplication by x.

$$A=\frac{B+I}{x}$$

Solve for B

$$B=Ax-I$$

Steps for Solving Linear Equation

Subtract Ax from both sides.

$$-B=I-Ax$$

Divide both sides by -1.

$$\frac{-B}{-1}=\frac{I-Ax}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$B=\frac{I-Ax}{-1}$$

Divide I-Ax by -1.

$$B=Ax-I$$