`A=[{:(3,1),(0,4):}]and B = [{:(1,1),(0,2):}]`, then which of the following is/are correct ?
I. AB is defined
II. BA is defined
III. AB = BA
Select the correct answer using the codes given below.

Options

A. Only I
B. Only II
C. Both I and II
D. I, II and III

Answer

D

Explanation

Let `A=[{:(3,1),(0,4):}]and B =[{:(1,1),(0,2):}]`
Now, `AB=[{:(3,1),(0,4):}][{:(1,1),(0,2):}]=[{:(3,5),(0,8):}]`
`and BA = [{:(1,1),(0,2):}][{:(3,1),(0,4):}]=" "[{:(3,5),(0,8):}]`
`rArr" "AB = BA`
Hence, all the three statements are correct.