Solve (lambdaI-A)=0

$$( \lambda I - A ) = 0$$

Solve for A

$$A=I\lambda$$

Solution Steps

Subtract \lambda I from both sides. Anything subtracted from zero gives its negation.

$$-A=-\lambda I$$

Cancel out -1 on both sides.

$$A=\lambda I$$

Solve for I

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

Steps for Solving Linear Equation

Add A to both sides. Anything plus zero gives itself.

$$\lambda I=A$$

Divide both sides by \lambda .

$$\frac{\lambda I}{\lambda }=\frac{A}{\lambda }$$

Dividing by \lambda undoes the multiplication by \lambda .

$$I=\frac{A}{\lambda }$$