For each conjecture, determine whether the conjecture is true or false. If the conjecture is true, state an appropriate theorem or propositon and prove it. If a conjecture is not true, provide a counterexample to show that it is false.Consider a square array of natural numbers whose rows, columns, and diagonals all sum to the same number. For example, the following is a 3 by 3 square where the sum of the 3 numbers in each row is equal to 15 , the sum of the numbers in each column is equal to 15 and the sum of the diagonals is 15 .

Complete either (a) or (b)
(a) Conjecture: Using only the digits 1 through 9 one time each, the 3 by 3 square below can be completed to form a square with all rows, columns, and diagonals summing to the same number.
(b) Conjecture: The 4 by 4 square below can be completed to form a square with all rows, columns, and diagonals summing to the same number.