(a) If R is the ring of all 2 X 2 matrices over Z, then for any A R, (x A)(x A) x 2 A 2 R x (b) There exist C,A R such that (C A)(C A) C 2 A 2 Therefore, Corollary 5 6 is false if the rings involved are not commutative ...

The given statement consists of two parts related to the properties of matrices over the ring of 2 x ...

(a) If R is the ring of all 2 X 2 matrices over Z, then for any...

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(a) If R is the ring of all 2 X 2 matrices over Z, then for any A ϵ R, (x + A)(x - A) = x² - A² ϵ R[x].

(b) There exist C,A ϵ R such that (C + A)(C - A) ≠ C² - A²• Therefore, Corollary 5.6 is false if the rings involved are not commutative.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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(a) If R is the ring of all 2 X 2 matrices over Z, then for any...

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