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

If then

The determinant of is .

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.

Simplify each element of the matrix .

Rearrange .

Rearrange .

Multiply by each element of the matrix.

Simplify each element of the matrix .

Rearrange .

Rearrange .

Rearrange .

Rearrange .

Assuming that is the matrix to solve for, multiply the inverse matrix by both sides of the equation .

Multiply each row in the first matrix by each column in the second matrix .

Simplify each element of the matrix by multiplying out all the expressions.

Multiplying the identity matrix by any matrix is matrix .

Multiply each row in the first matrix by each column in the second matrix .

Simplify each element of the matrix by multiplying out all the expressions.

is in the most simplified form.

Solving for the variables in , the answer is .

Solving for the variables in , the answer is .

Solve [[-6,3],[3,5]][[x,-2],[y,-6]]=[[27,-6],[-7,-36]]