Intro to Modular Arithmetic and Algebra Review

A group (M,*) is said to be abelian if

• (x+y)=(y+x)

• (x*y)=(y*x)

• (x+y)=x

• (y*x)=(x+y)

Matrix multiplication is a/an _________ property.

• Commutative

• Associative

• Additive

• Disjunctive

A cyclic group is always

• abelian group

• monoid

• semigroup

• subgroup

How many properties can be held by a group?

• 2

• 3

• 5

• 4

{1, i, -i, -1} is

• semigroup

• subgroup

• cyclic group

• abelian group

25 + 37 ≡ _____ mod 12

• 2

• 3

• 1

• 62

What does 144 reduce to mod 11?

• 144 mod 11

• 1 mod 11

• 2 mod 11

• 143 mod 11

Find the product 23 • 43 modulo 8

• 3 mod 8

• 4 mod 8

• 5 mod 8

• 6 mod 8

[(-5) · 6](mod 7)

• -5 mod 7

• 5 mod 7

• -2 mod 7

• 1 mod 7

19 = 77 (mod 5)

• True

• False