# Identity in Binary Operation

## Trending Questions

**Q.**

Number of circular permutations of n distinct objects is

n!

(n-1)!

**Q.**

Is matrix multiplication associative?

**Q.**Binary operation ∗ on R−{−1} defined by a∗b=ab+1 is

- ∗ is associative and commutative
- ∗ is associative but not commutative
- ∗ is neither associative nor commutative
- ∗ is commutative but not associative

**Q.**

$\left\{n(n+1)(2n+1):n\xe2\u02c6\u02c6Z\right\}$is a subset of

$6K:K\xe2\u02c6\u02c6Z$

$12K:K\xe2\u02c6\u02c6Z$

$18K:K\xe2\u02c6\u02c6Z$

$24K:K\xe2\u02c6\u02c6Z$

**Q.**

tan inverse x^2 + y^2 = a^2 find dy/dx

**Q.**

Identity of zero under multiplication is zero, because 0 ∗ 0 = 0 = 0 ∗ 0

True

False

**Q.**If * is defined on the set Ro ofall nonâˆ’zero real numbers by a*b=a+bâˆ’5, the identity elementin R for the binary operation * is

**Q.**Given a non-empty set X , consider the binary operation *: P( X ) × P( X ) → P( X ) given by A * B = A ∩ B &mnForE; A , B in P( X ) is the power set of X . Show that X is the identity element for this operation and X is the only invertible element in P( X ) with respect to the operation*.

**Q.**

Which equation illustrates the identity property of multiplication?

$(\mathrm{a}+\mathrm{bi})\xc3\u2014\mathrm{c}=(\mathrm{ac}+\mathrm{bci})$

$(\mathrm{a}+\mathrm{bi})\xc3\u20140=0$

$(\mathrm{a}+\mathrm{bi})\xc3\u2014(\mathrm{c}+\mathrm{di})=(\mathrm{c}+\mathrm{di})\xc3\u2014(\mathrm{a}+\mathrm{bi})$

$(\mathrm{a}+\mathrm{bi})\xc3\u20141=(\mathrm{a}+\mathrm{bi})$

**Q.**Find which of the operations given above has identity.

**Q.**

Identity of the binary operation subtraction is 0

False

True

**Q.**On Q−{1}, ∗ be the binary operation defined as a∗b=ab+1. Then the identity element for ∗ on Q−{1} is

- a−1a
- 11+a
- 11−a
- a+1a

**Q.**Let A = N × N and * be the binary operation on A defined by ( a , b ) * ( c , d ) = ( a + c , b + d ) Show that * is commutative and associative. Find the identity element for * on A, if any.

**Q.**Given a non-empty set X, consider the binary operation

∗P(X)×P(X)→P(X) given by

A∗B=A∩B, ∀A, B in P(X) is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation *.

**Q.**Let ∗ be a binary operation defined on R by a∗b=a+b4 ∀ a, b∈R, then the operation ∗ is

- Commutative and Associative
- Commutative but not Associative
- Associative but not Commutative
- Neither Associative nor Commutative

**Q.**

Let A=N×N and ∗ be the binary operation on A defined by (a, b)∗(c, d)=(a+c, b+d). Show that ∗ is commutative and associative. Find the identity element for ∗ on A, if any.

**Q.**The identity of the binary operation * defined by a∗b=ab4 is equal to

- 1
- 2
- 4

**Q.**

Let S = Z x (Z - {0}) and the binary operation * is defined as (a , b) * (c , d) = (ad + bc , bd) for all a, b, c, d ϵZ. The identity element of of S for the binary operation * on S is __

(1, 0)

(a, b)

(b, a)

(0, 1)

**Q.**

Let ∗ be a binary operation on the set Q of rational number as follows:

(i)a∗b=a−b

(ii)a∗b=a2+b2

(iii)a∗b=a+ab

(iv)a∗b=(a−b)2

(v)a∗b=ab4

(vi)a∗b=ab2

Show that none of the operation has identity.

**Q.**

Let ∗ be a binary operation on the set Q of rational number as follows:

(iv)a∗b=(a−b)2

Show that none of the operations has an identity.

**Q.**$\left|\begin{array}{ccc}a+b+c& -c& -b\\ -c& a+b+c& -a\\ -b& -a& a+b+c\end{array}\right|=2\left(a+b\right)\left(b+c\right)\left(c+a\right)$

**Q.**The binary operation ∗ defined on R as a∗b=1 ∀ a, b∈R is

- both associative and commutative
- commutative but not associative
- neither associative nor commutative
- associative but not commutative

**Q.**

Let ∗ be a binary operation on the set Q of rational number as follows:

(iii)a∗b=a+ab

Show that none of the operations has an identity.

**Q.**Let ∗ be a binary operation on R defined by a∗b=a+b−ab. If x∗5=3, then the value of x is

- −12
- −13
- 35
- 12

**Q.**A binary operation ∗ defined Q−{1} is given by a∗b=a+b−ab. Find the identity element.

**Q.**

Let ∗ be a binary operation on the set Q of rational number as follows:

(i)a∗b=a2+b2

Show that none of the opeartion has identity.

**Q.**

Given non-empty set X, consider the binary operation ∗:P(X)×P(X)→P(X) given by A∗B=A∩B∀A, B in P(X), where P(X)is the power set of X. Show that X is the identity element for this operation and X is the only invertible element in P(X) with respect to the operation.

**Q.**

Let ∗ be the binary operation on N defined by a∗b=HCF of a and b. Is ∗ commutative? Is ∗ associative? Does there exist identity for this binary operation on N?

**Q.**If * is a binary operation defined on A=N x N, by (a, b) * (c, d)=(a+c, b+d), prove that * is both commutative and associative. Find the identity if it exists.

**Q.**Let R0 denote the set of all non-zero real numbers and let A=R0×R0. If ′∗′ is a binary operation on A defined by (a, b)∗(c, d)=(ac, bd) for all (a, b)(c, d)∈A.

Find the identity element in A.