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.
References
Faizah, H. (2019). Pemahaman Mahasiswa tentang Konsep Grup pada Mata Kuliah Struktur Aljabar. MUST: Journal of Mathematics Education, Science and Technology, 4(1), 23. https://doi.org/10.30651/must.v4i1.2267
Khasanah, L., & Irawanto, B. (2011). Menentukan Invers Drazin dari Matriks Singular. Jurnal Matematika, 14(3), 137–142.
Leon, S. J. (2001). Aljabar Linear dan Aplikasinya (5th ed.). Erlangga.
Mudjiyanto, B. (2018). Tipe Penelitian Eksploratif Komunikasi. Jurnal Studi Komunikasi Dan Media, 22(1), 65–74. https://doi.org/10.31445/jskm.2018.220105
Pikatan, S. (1997). Pseudo-Identitas dan Pseudo-Invers Matriks Singular. Integral, 2(1), 11–14.
Rachmawati, I. (2012). Eksplorasi Etnomatematika Masyarakat Sidoarjo. MATHEdunesa, 1(1).
Sripatmi, Arjudin, & Septriana, A. Y. (2018). Aljabar Abstrak. Fakultas Keguruan dan Ilmu Pendidikan, Universitas Mataram.
Suhendry, & Suryani, I. (2015). Menentukan Invers Drazin dari Matriks Singular Dengan Metode Leverrier Faddeev. I(1), 27–38.
Yuliza, E., Amran, A., & Triyani. (2018). Implementasi Invers Matriks Tergeneralisasi pada Sistem Persamaan Linier. Anual Research Seminar 2018, 4(1), 978–979.
