Let M2x2 (R) be the set of all matrices with dimension 2 × 2, whose entries are all real numbers. Prove that(M2x2(R), +, x) is a ring, if + and x are the addition and multiplication operations on (2×2)-dimension matrices,respectively.

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Let M2x2(R) be the set of all matrices with dimension 2 × 2, whose entries are all real numbers. Prove that (M2×2(R),+, ×) is a ring, if + and x are the addition and multiplication operations on (2 x2)-dimension matrices, respectively.

Let M2x2(R) be the set of all matrices with dimension 2 × 2, whose entries are all real numbers. Prove that (M2×2(R),+, ×) is a ring, if + and x are the addition and multiplication operations on (2 x2)-dimension matrices, respectively.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let M2x2 (R) be the set of all matrices with dimension 2 × 2, whose entries are all real numbers. Prove that
(M2x2(R), +, x) is a ring, if + and x are the addition and multiplication operations on (2×2)-dimension matrices,
respectively.

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