Let n be a positive integer. An n×n matrix (a rectangular array of numbers with n rows and n columns) is said to be a platinum matrix if:[*] the n2 entries are integers from 1 to n;
[*] each row, each column, and the main diagonal (from the upper left corner to the lower right corner) contains each integer from 1 to n exactly once; and
[*] there exists a collection of n entries containing each of the numbers from 1 to n, such that no two entries lie on the same row or column, and none of which lie on the main diagonal of the matrix.Determine all values of n for which there exists an n×n platinum matrix. linear algebramatrixcombinatorics