State which of the following statements are true 10 and which are false. Given r

Question

State which of the following statements are true 10 and which are false. Given reasons for your answer: (a) The eigen values of a matrix A elementof SO_3 are 1 and -1. (b) There exists only one injective homomorphism between two free groups (c) There exists an irrational number alpha such that both alpha and alpha^2 satisfy a cubic polynomial with rational coefficients. (d) If G is a non-abelian group, then it has no irreducible representations. (e) Any cubic irreducible polynomial in F_7[x] must divide x^7 - x.

Explanation / Answer

a ) ans it is false because given here is not a matrix representation

b) no its false beacuse there exsits many hormorpshim between two free groups

c) yes it strue by using alpha and alpha square values only cubic polynomial with reflection coefficents

d) false because it has one dimentional representations

e) yes true it sstandard notation

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