Prove that the set of all m×n matrices having their elements as integers is a infinite abelian group

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Show that the set of all integers forms a group with respect to binary operation def. by a*b=a+b+1

Matrix Groups (Abstract Algebra)

Prove that the set of all even integers is an infinite abelian group under addition of integers

Prove that the set of all even integers is infinite abelian group under addition of integers

Prove that set I of all integer with the binary operation'*'defined by a*b=a+b+1 is an abelian group

Group Theory| Lecture 11| Set of matrices is an abelian group under matrix addition |Theta Classes

Prove :set of all non-zero complex no’s is infinite abelian grp under multiplication of complex no’s

Prove that set G is a group under ordinary matrix multiplication.