Pembentukan Grup Matriks Singular 2×2

Abstract

The study aims to determine the set of the singular matrix 2×2 that forms the group and describes its properties. The type of research was used exploratory research. Using diagonalization of the singular matrix S, whereas a generator matrix, pseudo-identity, and pseudo-inverse methods, we obtained a group singular matrix 2×2 with standard multiplication operations on the matrix, with conditions namely: (1) closed, (2) associative, (3) there was an element of identity, (4) inverse, there was (A)-1 so A x (A)-1 = (A)-1 x A = Is. The group was the abelian group (commutative group). In addition, in the group, Gs satisfied that if Ɐ A, X, Y element Gs was such that A x X = A x Y then X = Y and X x A = Y x A then X = Y. This show that the group can be applied the cancellation properties like the case in nonsingular matrix group. This research provides further research opportunities on the formation of singular matrix groups 3×3 or higher order.