1. The problem statement, all variables and given/known data Is the following a vector space? The set of all unit lower triangular 3 x 3 matrices [1 0 0] [a 1 0] [b c 1] 2. Relevant equations Properties of vector spaces 3. The attempt at a solution I checked the properties of vector space (usual addition and scalar multiplication). I proved that the upper triangular 3 x 3 matrices are vector spaces as they suffice all the properties of vector space. But I am not quite confident about lower triangle.