Inverse in Binary Operation

Q.

A binary operation can have inverse without identity

1. True

2. False

Q. Define a binary operation *on the set {0, 1, 2, 3, 4, 5} as Show that zero is the identity for this operation and each element a ≠ 0 of the set is invertible with 6 − a being the inverse of a .

Q. The inverse of the number 5 with respect to the binary operation * defined by $a\ast b=4ab$ is .

1. $\frac{1}{80}$
2. $\frac{1}{5}$
3. $\frac{1}{20}$

Q.

A binary operation can have inverse without identity

1. False

2. True

Q. A binary operation can result in an inverse for a number even in the absence of an identity

1. True
2. False

Q.

Which of the following is the inverse pair of 1 under the operations multiplication and subtraction?

1. 1, 0

2. 1, 1

3. 0, 0

4. None of these

Q.

Which of the following is the inverse pair of 1 under the operations multiplication and subtraction?

1. 1, 1

2. 1, 0

3. 0, 0

4. None of these

Q.

Which of the following is the inverse pair of 1 under the operations multiplication and subtraction?

1. 1, 1

2. 1, 0

3. 0, 0

4. None of these