April 2026

Prove that the operation * on the set M = { [[a 0][0 b]] : a, b ∈ R – {0} } defined by A*B = AB is a binary operation.

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Binary Operation on Matrix Set 📺 Watch Video Explanation: Prove that the operation is a binary operation Given: Set \( M = \left\{ \begin{bmatrix} a & 0 \\ 0 & b \end{bmatrix} : a, b \in \mathbb{R} – \{0\} \right\} \) Operation defined by: \( A * B = AB \) Concept: To prove a […]

Prove that the operation * on the set M = { [[a 0][0 b]] : a, b ∈ R – {0} } defined by A*B = AB is a binary operation. Read More »

Is * defined on the set {1,2,3,4,5} by a*b = LCM of a and b a binary operation? Justify your answer.

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Binary Operation using LCM 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: Set \( S = \{1,2,3,4,5\} \) and operation defined by \( a * b = \mathrm{LCM}(a,b) \) Concept: A binary operation must satisfy the closure property, i.e., the result must belong to the same set. Solution:

Is * defined on the set {1,2,3,4,5} by a*b = LCM of a and b a binary operation? Justify your answer. Read More »

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = a + 4b^2 Here, Z + denotes the set of all non-negative integers.

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Binary Operation on Real Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( * \) on \( \mathbb{R} \) defined by \( a * b = a + 4b^2 \quad \forall \, a, b \in \mathbb{R} \) Concept: A binary operation must satisfy the closure

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = a + 4b^2 Here, Z + denotes the set of all non-negative integers. Read More »

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = a Here, Z + denotes the set of all non-negative integers.

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Binary Operation on Non-Negative Integers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: The set \( \mathbb{Z}^+ = \{0,1,2,3,\dots\} \) and operation \( * \) defined by \( a * b = a \quad \forall \, a, b \in \mathbb{Z}^+ \) Concept: A binary operation must satisfy the

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = a Here, Z + denotes the set of all non-negative integers. Read More »

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = |a – b| Here, Z + denotes the set of all non-negative integers.

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Binary Operation on Non-Negative Integers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: The set \( \mathbb{Z}^+ = \{0,1,2,3,\dots\} \) and operation \( * \) defined by \( a * b = |a – b| \quad \forall \, a, b \in \mathbb{Z}^+ \) Concept: A binary operation must

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = |a – b| Here, Z + denotes the set of all non-negative integers. Read More »

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = ab^2 Here, Z + denotes the set of all non-negative integers.

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Binary Operation on Real Numbers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: An operation \( * \) on \( \mathbb{R} \) defined by \( a * b = ab^2 \quad \forall \, a, b \in \mathbb{R} \) Concept: A binary operation must satisfy the closure property, meaning

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On R, defined * by a*b = ab^2 Here, Z + denotes the set of all non-negative integers. Read More »

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = ab Here, Z + denotes the set of all non-negative integers.

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Binary Operation on Non-Negative Integers 📺 Watch Video Explanation: Determine whether the operation is a binary operation or not Given: The set \( \mathbb{Z}^+ = \{0,1,2,3,\dots\} \) (non-negative integers) and operation \( * \) defined by \( a * b = ab \quad \forall \, a, b \in \mathbb{Z}^+ \) Concept: A binary operation must

Determine whether or not each definition * given below gives a binary operation. In the event that * is not a binary operation give justification of this. On Z + , defined * by a*b = ab Here, Z + denotes the set of all non-negative integers. Read More »