Solve a^-1=1/a

$$a ^ { - 1 } = \frac { 1 } { a }$$

Solve for a

$$a\neq 0$$

Solution Steps

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$aa^{-1}=1$$

Subtract 1 from both sides.

$$aa^{-1}-1=0$$

Reorder the terms.

$$-1+\frac{1}{a}a=0$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by a.

$$a\left(-1\right)+1a=0$$

Combine a\left(-1\right) and 1a to get 0.

$$0=0$$

Compare 0 and 0.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Variable a cannot be equal to 0.

$$a\in \mathrm{R}\setminus 0$$