Solve |a*B|=|a|*|0|

$$| a \cdot B | = | a | \cdot | 0 |$$

Solve for B

$$\left\{\begin{matrix}\\B=0\text{, }&\text{unconditionally}\\B\in \mathrm{R}\text{, }&a=0\end{matrix}\right.$$

Steps Using Definition of Absolute Value

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$|aB|=|a|\times 0$$

Reorder the terms.

$$|Ba|=0$$

Combine like terms and use the properties of equality to get the variable on one side of the equal sign and the numbers on the other side. Remember to follow the order of operations.

$$|aB|=0$$

Use the definition of absolute value.

$$aB=0$$

Divide both sides by a.

$$B=0$$

Solve for a

$$\left\{\begin{matrix}\\a=0\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&B=0\end{matrix}\right.$$

Steps Using Definition of Absolute Value

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 0 is 0.

$$|aB|=|a|\times 0$$

Subtract |a|\times 0 from both sides.

$$|aB|-|a|\times 0=0$$

Reorder the terms.

$$|Ba|=0$$

Use the definition of absolute value.

$$Ba=0$$

Divide both sides by B.

$$a=0$$