Consider a set of n linear equations in n unknowns x₁, x₂,…, x_n, written in matrix form as Ax = b. When A is invertible, the set of equations has a unique solution x = A⁻¹b. Since A⁻¹ = (1/detA) adjA, where adjA is the adjoint of A, this gives the solution

which may be written

using the entries of b and the cofactors of A. This is Cramer’s rule. Computationally Cramer’s rule is highly inefficient compared with Gaussian elimination.