On determinants of matrices related to Pascal’s triangle

Abstract

We prove that the symmetric Pascal triangle matrix modulo 2 has the property that each of the square sub-matrices positioned at the upper border or on the left border has determinant, computed in \({\mathbb {Z}}\), equal to 1 or \(-1\). Furthermore, we give the exact number of Pascal-like \(n \times m\) matrices over a commutative ring with finite group of units.