# 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

Add and .

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

Multiply by each element of the matrix.

Step 6

Step 6.1

Multiply by .

Step 6.2

Multiply by .

Step 6.3

Combine and .

Step 6.4

Move the negative in front of the fraction.

Step 6.5

Cancel the common factor of .

Step 6.5.1

Cancel the common factor.

Step 6.5.2

Rewrite the expression.