Question 4 [8 marks] UNSW runs many competitions throughout the year but the one that caught Kim's attention is the UNSW Math Olympiad. Kim participated t of in this competition because it offers the biggest prize money (AUD 1 million). Having learned math in ECON1202, Kim is ready to show all UNSW students and the whole world that she has "beauty and brains". The win condition is simple. The contestant that completes all of the following challenges in the shortest amount of time will be the winner. Challenge 1 Consider the following matrix: b A = d g h All entries are integers Statement I: If a = 6g, b = 6h and c = 6i, A-1 (No answer given) regardless of the values of d,e,f Statement II: If we modify the matrix by multiplying each of the entries a, b,c by 6 and multiplying each of the entries g,h,i by 6, then the determinant of the matrix becomes multiplied by (enter a numerical value in the box provided) Statement III: [AATI = [ATAI. (No answer given) Statement IV: Assume that A is an upper triangular matrix. If the determinant of A is 64 and a = e = i, then the value of each of the diagonal entries is (enter a numerical value in the box provided)