Examples

Find the Inverse
Step 1
The inverse of a matrix can be found using the formula where is the determinant.
Step 2
Find the determinant.
Tap for more steps...
Step 2.1
The determinant of a matrix can be found using the formula .
Step 2.2
Simplify the determinant.
Tap for more steps...
Step 2.2.1
Simplify each term.
Tap for more steps...
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
Divide by .
Step 6
Multiply by each element of the matrix.
Step 7
Simplify each element in the matrix.
Tap for more steps...
Step 7.1
Multiply by .
Step 7.2
Multiply by .
Step 7.3
Multiply by .
Step 7.4
Multiply by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.