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 .

Multiply and .

Multiply by .

Multiply by .

Multiply .

Multiply and .

Multiply by .

Multiply by .

Combine the numerators over the common denominator.

Subtract from .

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 of the Matrix [[40/13,70/13],[28/13,140/13]]