inverse matrix

Given the basis of some vector space V, how to find its dual basis, i.e., the basis of the dual space V^*? Fill the columns of a square matrix M with the basis vectors of V. Find the inverse matrix M⁻¹ of M. Then the rows of M⁻¹ are the (co)vectors of that dual basis. Since (M⁻¹)⁻¹=M, then (V^*)^*=V.