2. A diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the upper left corner to the lower right corner. Formally, an nxn matrix A = [aij) is diagonal if Qij = 0 whenever i + j. Equivalently, if Wij 70 then i =j. An anti-diagonal matrix is a square matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner. Formally, an nx n matrix A= [dij] is anti-diagonal if Qij = 0 whenever i+in+1. Equivalently, if Qij 70 then i + j=n+1. Prove that the product of two nxn anti-diagonal matrices is diagonal. (See outline below, also the proof in #13 of homework 2.1) Outline: (1) Begin your proof by letting A = [ajland B = [bi] be two anti-diagonal n X n matrices. To prove that the matrix AB is diagonal you need to show that the ij-th entry of AB is O for all i + j, or, equivalently, if the ij-th entry of AB is not 0, then i = j. (this second part is the one to use). (ii) The ij-th entry of the product AB is cj = (write in terms of ) (iii) Show that if Cij #0 (*) then i =j. * HINT: there must be at least one term dikbkj that is not 0