Solve A*x=A-I

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

Solve for A (complex solution)

$$\left\{\begin{matrix}A=-\frac{I}{x-1}\text{, }&x\neq 1\\A\in \mathrm{C}\text{, }&I=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract A from both sides.

$$Ax-A=-I$$

Combine all terms containing A.

$$\left(x-1\right)A=-I$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)A}{x-1}=-\frac{I}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$A=-\frac{I}{x-1}$$

Solve for A

$$\left\{\begin{matrix}A=-\frac{I}{x-1}\text{, }&x\neq 1\\A\in \mathrm{R}\text{, }&I=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract A from both sides.

$$Ax-A=-I$$

Combine all terms containing A.

$$\left(x-1\right)A=-I$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)A}{x-1}=-\frac{I}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$A=-\frac{I}{x-1}$$

Solve for I

$$I=A\left(1-x\right)$$

Steps for Solving Linear Equation

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

$$A-I=Ax$$

Subtract A from both sides.

$$-I=Ax-A$$

Divide both sides by -1.

$$\frac{-I}{-1}=\frac{A\left(x-1\right)}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$I=\frac{A\left(x-1\right)}{-1}$$

Divide A\left(-1+x\right) by -1.

$$I=A-Ax$$