# Let β ={x1,...,xn} be a subset of Fn containing n distinct vectors, and let B denote the element of Mnxn (F) whose jth column is the vector xj. Prove that β is a basis for Fn if and only if det(B) ≠ 0.

Question

Let β ={x1,...,xn} be a subset of Fn containing n distinct vectors, and let B denote the element of Mnxn (F) whose jth column is the vector xj. Prove that β is a basis for Fn if and only if det(B) ≠ 0.