Solution Found!
Let M2(Z) be the ring of all 2 × 2 matrices over the
Chapter 12, Problem 40E(choose chapter or problem)
Let M2(Z) be the ring of all 2 × 2 matrices over the integers and let R = Prove or disprove that R is a subring of M2(Z).
Questions & Answers
QUESTION:
Let M2(Z) be the ring of all 2 × 2 matrices over the integers and let R = Prove or disprove that R is a subring of M2(Z).
ANSWER:Step 1 of 4
A ring R is a set with two binary operations, addition and multiplication, satisfying several properties: R is an Abelian group under addition, and the multiplication operation satisfies the associative law.
According to the distributive law,
Also,
For every
The identity of the addition is denoted as 0. If the multiplication operation has an identity. It is also termed as unity. R is said to be commutative if the multiplication is commutative.