Sir i am stuck for this question

1.1 Part a: covariance matrix Let X1, ..., Xn be p-dimensional data and write matrix X E R"XP where the X; is the i-th row of X. Assume that X is centered in the sense that every column has mean zero: Xij = 0 for all columns j = 1, . . ., p. First, use Homework 1 to show that n X X = XXXJ. i=1 Now, use this to show that 1X X is the empirical covariance matrix: (,XTX) ;k = - Ell XijXik. In other words, the (j, k) entry of _ X X is the empirical covariance be- tween feature j and feature k. Side note: normally, the covariance between feature j and feature k is - Et_,(Xij - X.;)(Xik - Xik) where X.j = 1 El_, Xij and X.k = _ _ _] Xix. Here, because we assume that all the features are centered, we have that X.; =0 and X.k = 0