Every elementary matrix E has an inverse, and E 1 is also elementary. EDIT. (Writing an invertible matrix as a product of elementary matrices) If A is invertible, the theorem implies that A can be written as a product of elementary matrices.To do this, row reduce A to the identity, keeping track of the row operations you're using. The calculator can find an inverse matrix directly (if it exists): 011 221 001 − − MATRIX NAMES 1:[A] ENTER x–1 ENTER MATH MATH 1: