This is the first time I'm posting (or rather asking) anything here. I'm a student of elementary linear algebra, therefore plz excuse me if my questions come across as dumb or if I make any mistakes: I have a question about determinants and whether or not a solution exists, etc. I will be focusing on square matrices only: If the determinant of a matrix is not equal to zero, then does that mean the matrix has a unique solution? If the determinant is equal to zero, then either the matrix has infinitely many solutions or no solution, correct? And if it is a homogeneous system, then the system has infinitely many solutions if the determinant is equal to zero, correct? Thanking you in advance, Bye. P.S. Could someone kindly tell me what is meant by singular and non-singular matrices?