# inverse matrix

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