Suppose X and Y are rings and that f : X → Y is an isomorphism. Let X2x2 be the set of all 2 × 2 matrices with components from X and Y2x2 the set of all 2 × 2 matrices with components from Y. Show that X2x2 and Y2×2 are also isomorphic by completing parts below. Define g: X2x2 → Y2x2 by [f(a) f(b)] [f(c) d f(d) Show that g is a homomorphism.

Suppose X and Y are rings and that f : X → Y is an isomorphism. Let X2x2 be the set of all 2 × 2 matrices with components from X and Y2x2 the set of all 2 × 2 matrices with components from Y. Show that X2x2 and Y2×2 are also isomorphic by completing parts below. Define g: X2x2 → Y2x2 by [f(a) f(b)] [f(c) d f(d) Show that g is a homomorphism.

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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