Find the order of the given factor group (Z3 x Z6)/<(1,1)>

Q1: Check whether (K,*) forms a group, where "* "refers to the matrix multiplication and K = {h₁, h₂, h3, h4}. Represent the properties in table form. Here, m₁ = ( 9 ), h₂ = ( 1), h3 = (₁-¹) and h₁ = (¹9).

Which answer is correct?

Z12 The order of the element 5+ (4) in the factor group is (4) a) 12 b) 5 c) 4 d) 0

The factor group U(16)/(9)has an element of order 4. True of false? True O Falsc

In point group D2d, for each of the irreducible representations, verify that the sum of the squares of the characters equals the order of the group.

Find the order of the element 5(9)in the factor group U(16)/(9).

Use Algorithm 3.2 (Divided Difference) to construct the interpolating polynomial of degree three for the following data: f(1) = 1.2,f(2)= 1.6,f(4)=2, and f(5)=2.6 , then f(2.6)

give the order of the element in the factor group (2,0) + <(4,4)> in (Z6 x Z8)/<(4,4)>