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Math / Contemporary Abstract Algebra 8 / Chapter 12 / Problem 42E

Contemporary Abstract Algebra | 8th Edition | ISBN: 9781133599708 | Authors: Joseph Gallian

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Let Prove or disprove that R is a subring of M2(Z)

Chapter 12, Problem 42E

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QUESTION:

Let Prove or disprove that R is a subring of M2(Z)

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QUESTION:

Let Prove or disprove that R is a subring of M2(Z)

ANSWER:

Step 1 of 3

A ring R is a set with two binary operations that is addition and multiplication which satisfies the properties, R is an Abelian group under addition, and the multiplication operation satisfies the associative law and distributive laws.

The associative law is,

The distributive laws,

for every

The identity of the addition operation is 0. If the multiplication operation has an identity, it is called a unity. If multiplication is commutative then R is commutative.

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