If A is m x n, then the matrix G = A^TA is called the Gram matrix of A. In this case, the entries of G are the inner products of the columns of A. 

a. Show that the Gram matrix of any matrix A is positive semidefinite, with the same rank as A.

b. Show that if the columns of A are linearly independent, then G is invertible. Explain how the Gram matrix can be used in this case to compute the orthogonal projection onto Col A.