Vedic Maths - Multiplication by Series of 9's

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.

Name the property of multiplication of rational number illustrated by the statement: (-5)/9×\ (4/(15)×(-9)/8)=((-5)/9×4/(15))×(-9)/8

Name the property of multiplication of rational number illustrated by the statement: (-17)/5×\ 9=9×(-17)/5

Name the multiplication property of rational numbers shown below : (v) (8)/(-9)xx1=1xx(8)/(-9)=(8)/(-9)

Name the multiplication property of rational numbers shown below : (i) (3)/(5)xx(-8)/(9)=(-8)/(9)xx(3)/(5)

For pair of rational numbers, given below, verify that the multiplication is commutative : (-1)/(5) "and" (2)/(9)

Solve, using cross - multiplication : x - y + 2 = 0 7x + 9y = 130

For each pair of rational numbers, given below, verify that the multiplication is commutative : (iii) 3 "and" (-8)/(9)

find the multiplicative inverse of the complex number 2 + 9i .

Solve, using cross - multiplication : 4x - 7y + 28 = 0 and -7x + 5y + 9 = 0 .