On determinants of matrices related to Pascal’s triangle

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  \({\mathbb {Z}}\) $\mathbb{Z}$ , equal to 1 or  \(-1\) $-1$ . Furthermore, we give the exact number of Pascal-like \(n \times m\) $n\times m$ matrices over a commutative ring with finite group of units.