# Finite Math Examples

Step 1
The inverse of a matrix can be found using the formula where is the determinant.
Step 2
Find the determinant.
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
Multiply by each element of the matrix.
Step 6
Simplify each element in the matrix.
Step 6.1
Cancel the common factor of .
Step 6.1.1
Factor out of .
Step 6.1.2
Factor out of .
Step 6.1.3
Cancel the common factor.
Step 6.1.4
Rewrite the expression.
Step 6.2
Combine and .
Step 6.3
Cancel the common factor of .
Step 6.3.1
Factor out of .
Step 6.3.2
Factor out of .
Step 6.3.3
Cancel the common factor.
Step 6.3.4
Rewrite the expression.
Step 6.4
Combine and .
Step 6.5
Move the negative in front of the fraction.
Step 6.6
Cancel the common factor of .
Step 6.6.1
Factor out of .
Step 6.6.2
Factor out of .
Step 6.6.3
Cancel the common factor.
Step 6.6.4
Rewrite the expression.
Step 6.7
Combine and .
Step 6.8
Move the negative in front of the fraction.
Step 6.9
Combine and .