# Algebra Examples

Step 1

Add the corresponding elements.

Step 2

Step 2.1

Add and .

Step 2.2

Subtract from .

Step 2.3

Add and .

Step 2.4

Add and .

Step 3

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

Step 4

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

Step 9.1

Multiply .

Step 9.1.1

Multiply by .

Step 9.1.2

Combine and .

Step 9.2

Cancel the common factor of .

Step 9.2.1

Move the leading negative in into the numerator.

Step 9.2.2

Factor out of .

Step 9.2.3

Factor out of .

Step 9.2.4

Cancel the common factor.

Step 9.2.5

Rewrite the expression.

Step 9.3

Combine and .

Step 9.4

Multiply by .

Step 9.5

Multiply .

Step 9.5.1

Multiply by .

Step 9.5.2

Multiply by .

Step 9.6

Cancel the common factor of .

Step 9.6.1

Move the leading negative in into the numerator.

Step 9.6.2

Factor out of .

Step 9.6.3

Factor out of .

Step 9.6.4

Cancel the common factor.

Step 9.6.5

Rewrite the expression.

Step 9.7

Combine and .

Step 9.8

Multiply by .

Step 9.9

Move the negative in front of the fraction.