We identify the matrix first by the rows and then by the columns. The determinant of a matrix is the product of ad - bc. When this product is zero, then a matrix cannot have an inverse. Also, remember that a singular matrix is one that doesn't have an inverse because the product ab - bc = 0.
Similarly one may ask, when matrix is nonsingular?
A square matrix that is not singular, i.e., one that has a matrix inverse. Nonsingular matrices are sometimes also called regular matrices. A square matrix is nonsingular iff its determinant is nonzero (Lipschutz 1991, p. 45).
How can a matrix be singular?
A square matrix that does not have a matrix inverse. A matrix is singular iff its determinant is 0. For example, there are 10 singular (0,1)-matrices: The following table gives the numbers of singular matrices for certain matrix classes.
Can a non square matrix be nonsingular?
A square matrix that is not invertible is called singular or degenerate. A square matrix is singular if and only if its determinant is 0. Non-square matrices (m-by-n matrices for which m ≠ n) do not have an inverse. However, in some cases such a matrix may have a left inverse or right inverse.