Tables, multiplication, divide trick of 99

Use matrix multiplication to divide Rs. 30,000 in two parts such that the total annual interest at 9% on the first part and 11% on the second part amounts Rs. 3060

Complete the following multiplication table: Is the multiplication table symmetrical about the diagonal joining the upper left corner to the lower right corner?

Consider the set S={1,-1,i ,-i} for fourth roots of unity. Construct the composition table for multiplication on S and deduce its various properties.

Consider the set S={1,\ -1,\ i ,\ -i} of fourth roots of unity. Construct the composition table for multiplication on S and deduce its various properties.

Write the multiplication table for the set of integers modulo 5.

What is the value of additive identity of integers divided by multiplicative identity of integers?

Consider the set S={1,\ -1} of square roots of unity and multiplication (xx) as a binary operation on S Construct the composition table for multiplication (xx) on S Also, find the identity element for multiplication on S and the inverses of various elements.

Consider the set S={1,\ omega,\ omega^2} of all cube roots of unity. Construct the composition table for multiplication (xx) on Sdot Also, find the identity element for multiplication on Sdot Also, check its commutativity and find the identity element. Prove that every element of S is invertible.

What is multiple fission?

Complete the multiplication table given below: