Linear Algebra Course Notes 1. Matrix and Determinants 2 1.1
... (3) Existence of 0 There exists an element 0, such that for any elemnt a ∈ F ,a + 0 = a. (4) Existence of opposite For any element a ∈ F , There exists an element called −a, such that a + (−a) = 0 (5) Commutativity of × For any two elements a, b ∈ F , we have a × b = b × a (6) Associativity of × For ...
... (3) Existence of 0 There exists an element 0, such that for any elemnt a ∈ F ,a + 0 = a. (4) Existence of opposite For any element a ∈ F , There exists an element called −a, such that a + (−a) = 0 (5) Commutativity of × For any two elements a, b ∈ F , we have a × b = b × a (6) Associativity of × For ...
