[AntonioLao]

The definition of determinants shows that direct connection to the study of permutations which have eight theorems and one corollary. Theorem 1 says that if two numbers in the column index permutation of an n by n matrix are interchanged, the sign of the permutation is reversed. Theorem 2 says let the permutation j1,j2,…,jn be formed from 1,2, …,n by k successive interchanges then the sign of the permutation is negative if k is odd and positive if k is even. Theorem 3 says the determinant of a square matrix is equal to the determinant of its transpose. Theorem 4 says if two rows (columns) are interchanged then the sign of the determinant is reversed. Corollary says if two rows (columns) are identical, the determinant is zero. Theorem 5 says if a row (column) is multiplied by a constant, the determinant is multiplied by the same. Theorem 6 says if a multiple of one row (column) is subtracted from another row (column), the determinant is not changed. Theorem 7 says if aij=0 for i>j then the determinant is simply the product of the diagonal elements a11a22…ann. Theorem 8 says if aij=0 for i<j then the determinant is also the product of the diagonal elements a11a22…ann.

All these theorems suggest that the n by n time ordering matrix of the universe is simply the identity matrix. Its odd and even permutations switch the quantized values of its determinant as minus unity or plus unity. To assume that the universe begins at time zero is simply to apply theorem 5. The other option is to apply the corollary but then the time matrix loses its identity.