SYARAT PERLU DAN SYARAT CUKUP MATRIKS BERSIH PADA 𝕄𝕄𝟐𝟐(ℤ)

Abstract

This paper describes the condition of a net matrix at 𝕄𝕄2 (ℤ) and describes the terms and conditions of sufficient net matrix at 𝕄𝕄2 (ℤ). The result of this study is, 𝑨𝑨 is the 1-net matrix if and only if 𝑑𝑑𝑑𝑑𝑑𝑑 (𝑨𝑨) -𝑡 𝑡𝑡 (𝑨𝑨) = 0 or -2. Then 𝑨𝑨 is the 0-net matrix if and only if 𝑨𝑨 is the unit matrix, or satisfies one of the equations 𝑎𝑎𝑎 -𝑏𝑏𝑏𝑏-𝑑𝑑 + 𝑏𝑏𝑏𝑏 = ± 1, 𝑎𝑎𝑎 -𝑏𝑏𝑏𝑏-𝑎𝑎 + 𝑏𝑏𝑏𝑏 = ± 1, 􀵫-𝑏𝑏􀵯𝑤𝑤2 + ( 𝑎𝑎-𝑑𝑑) 𝑤𝑤𝑤𝑤 + (𝑐) 𝑥 2+ (𝑏𝑏) 𝑤𝑤 + (𝑎𝑎𝑎 -𝑏𝑏𝑏𝑏-𝑎𝑎 ± 1) 𝑥 = 0. And the requirement of 𝑨𝑨 is sufficient and 𝑨𝑨 is a 0-net matrix ie if 𝑩𝑩 = 􁉂𝑎𝑎𝑏𝑏00􁉃∈𝕄𝕄2 (ℤ) is a 0-net matrix then 𝑨𝑨 is a 0-net matrix.