Expert Help for Abstract Algebra Challenges

How many 3/4 Are in 1

6. Reduce the following matrix to reduced row echelon form:                                                                                                   

Let v be a vector over a field F with zero vector  0 and let s,T be a substance of V .then which of the following statements are false

Describe Aut(Zp), the automorphism group of the cyclic group Zp where p is prime. In particular find the order of this group. (Hint: A generator must map to another generator)

Let a and b belong to a ring R and let m be an integer. Prove that m(ab) = (ma)b = a(mb)

prove that the union of two subgroups is a subgroup iff one is contained in the other.

Determine if the given sequence is an arithmetic sequence. If it​ is, find the common​ difference, d.
−8​,-3, 2, 7, ...
 

If R is a commutative ring with unity 1 the R[x] is also a commutative ring with unity 1

${\displaystyle \frac{{\mathbb{F}}_2[X,Y]}{(Y^2+Y+1,X^2+X+Y)}}$ and $\frac{{\displaystyle \left({\mathbb{F}}_2\right[Y]}}{{\displaystyle (Y^2+Y+1)}}\frac{{\displaystyle \left)\right[X]}}{{\displaystyle (X^2+X+\overline{Y})}}$ are isomorphic