# Algebra Examples

Find the Inverse of the Resulting Matrix
Step 1
Step 2
Simplify each element.
Step 2.1
Step 2.2
Step 2.3
Step 2.4
Step 3
The inverse of a matrix can be found using the formula where is the determinant.
Step 4
Find the determinant.
Step 4.1
The determinant of a matrix can be found using the formula .
Step 4.2
Simplify the determinant.
Step 4.2.1
Simplify each term.
Step 4.2.1.1
Multiply by .
Step 4.2.1.2
Multiply by .
Step 4.2.2
Subtract from .
Step 5
Since the determinant is non-zero, the inverse exists.
Step 6
Substitute the known values into the formula for the inverse.
Step 7
Move the negative in front of the fraction.
Step 8
Multiply by each element of the matrix.
Step 9
Simplify each element in the matrix.
Step 9.1
Cancel the common factor of .
Step 9.1.1
Move the leading negative in into the numerator.
Step 9.1.2
Factor out of .
Step 9.1.3
Factor out of .
Step 9.1.4
Cancel the common factor.
Step 9.1.5
Rewrite the expression.
Step 9.2
Combine and .
Step 9.3
Multiply by .
Step 9.4
Move the negative in front of the fraction.
Step 9.5
Cancel the common factor of .
Step 9.5.1
Move the leading negative in into the numerator.
Step 9.5.2
Factor out of .
Step 9.5.3
Factor out of .
Step 9.5.4
Cancel the common factor.
Step 9.5.5
Rewrite the expression.
Step 9.6
Combine and .
Step 9.7
Multiply by .
Step 9.8
Cancel the common factor of .
Step 9.8.1
Move the leading negative in into the numerator.
Step 9.8.2
Factor out of .
Step 9.8.3
Factor out of .
Step 9.8.4
Cancel the common factor.
Step 9.8.5
Rewrite the expression.
Step 9.9
Combine and .
Step 9.10
Multiply by .
Step 9.11
Cancel the common factor of .
Step 9.11.1
Move the leading negative in into the numerator.
Step 9.11.2
Factor out of .
Step 9.11.3
Cancel the common factor.
Step 9.11.4
Rewrite the expression.
Step 9.12
Move the negative in front of the fraction.