tesler matrices are certain integral matrices counted by the kostant partition function and have appeared recently in haglund's study of diagonal harmonics. in 2014, drew armstrong defined a poset on such matrices and conjectured that the characteristic polynomial of this poset is a power of $(q-1)$. we will use a method of bruce sagan and joshua hallam to prove armstrong's conjecture and explore how this result can improve the bounds on the number of tesler matrices.