I'd like to know if the following two paragraphs regarding the determinant of a matrix are correct and also, am I missing any other important implications by calculating the determinant? any other important things I can find from with that value? thanks.
1. If det A=0 <=> Linear Dependence <=> Infinitely many solutions (hence non trivial solution) <=> non invertible (or singular) matrix <=> vectors are parallel.
2. If det A != 0 <=> L.I <=> unique solution <=> invertible (also nonsingular or regular) matrix