# Precalculus Examples

Step 1

The inverse of a matrix can be found using the formula where is the determinant.

Step 2

Step 2.1

The determinant of a matrix can be found using the formula .

Step 2.2

Simplify the determinant.

Step 2.2.1

Simplify each term.

Step 2.2.1.1

Multiply by .

Step 2.2.1.2

Multiply by .

Step 2.2.2

Subtract from .

Step 3

Since the determinant is non-zero, the inverse exists.

Step 4

Substitute the known values into the formula for the inverse.

Step 5

Move the negative in front of the fraction.

Step 6

Multiply by each element of the matrix.

Step 7

Step 7.1

Multiply .

Step 7.1.1

Multiply by .

Step 7.1.2

Multiply by .

Step 7.2

Cancel the common factor of .

Step 7.2.1

Move the leading negative in into the numerator.

Step 7.2.2

Factor out of .

Step 7.2.3

Factor out of .

Step 7.2.4

Cancel the common factor.

Step 7.2.5

Rewrite the expression.

Step 7.3

Combine and .

Step 7.4

Multiply by .

Step 7.5

Cancel the common factor of .

Step 7.5.1

Move the leading negative in into the numerator.

Step 7.5.2

Factor out of .

Step 7.5.3

Factor out of .

Step 7.5.4

Cancel the common factor.

Step 7.5.5

Rewrite the expression.

Step 7.6

Combine and .

Step 7.7

Multiply by .

Step 7.8

Cancel the common factor of .

Step 7.8.1

Move the leading negative in into the numerator.

Step 7.8.2

Factor out of .

Step 7.8.3

Factor out of .

Step 7.8.4

Cancel the common factor.

Step 7.8.5

Rewrite the expression.

Step 7.9

Combine and .

Step 7.10

Multiply by .

Step 7.11

Move the negative in front of the fraction.