(a) Recall that an idempotent matrix is a square matrix A such that A? = A. Show that if a and b are real numbers with b 0, then the matrix a b A = a(1 - a)/b 1 -a is idempotent. To obtain the marks, calculate each of the four entries of A2 separately, i.e., the (1, 1)-entry, (1, 2)-entry, and so on, and show the details of each calculation. (b) By adding an appropriate scalar multiple of the first row of A to the second, find rank(A). Make it clear what scalar you use and what calculations you do to arrive at your answer. (c) Is A invertible? Explain your answer. Hint: Use part (b), or compute the determinant of A