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

If then

These are both valid notations for the determinant of a matrix.

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

Simplify the determinant.

Simplify each term.

Multiply by .

Multiply by .

Subtract from .

Substitute the known values into the formula for the inverse of a matrix.

Rearrange .

Rearrange .

Multiply by each element of the matrix.

Rearrange .

Rearrange .

Rearrange .

Rearrange .

Find the Inverse [[0.4,-0.2],[-0.2,0.5]]