I am unable to understand the solution for this answer, what does the 3x3 matrix represent and why is there a need to find D1 and D?

4. Suppose that the following functions are used in optimization: (a) Z = XY (X, Y20) (b) Z = Y-InX (X, Yz0) Assuming that the first-order conditions for maximum or minimum hold in both cases, determine whether there is a maximum or minimum in each case. Answer (a) Z = XY (X, Y20) Zx = Y, Zy = X Zxx = 0, ZyY = 0, ZxY = 1, Zyx = 1 0 1 Y 1 OX = D = 2XY YX O Y D1 = =-Y'S0 Y 0 The function is quasi concave (maximum)