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.