Determinant of a Triangular Matrix

Expand the determinant by cofactors along the first column of a triangular matrix.

Each cofactor expansion collapses to the remaining diagonal entries.

1. 1. Expand by cofactors

   Cofactor expansion along the first column of a triangular matrix leaves only the term involving the top-left diagonal entry, since all other entries in that column are zero.

2. 2. Repeat recursively

   Applying this repeatedly to the remaining triangular submatrix shows the determinant equals the product of all diagonal entries.

Answer: The product of its diagonal entries.