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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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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 (M2x2(R), +, x) is a ring, if + and x are the addition and multiplication operations on (2×2)-dimension matrices, respectively.
Transcribed Image Text: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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