a.) Explain in your own words what this problem is asking.b.) Explain the meaning of any notation used in the problem and in your solution.c.) Describe the mathematical concept(s) that appear to be foundational to this problem.d.) Justified solution to or proof of the problem. **Transcription with Explanation**### Problem Statement:Prove or disprove that the set of all diagonal matrices in \( M_n(\mathbb{R}) \) forms a group with respect to addition.### Detailed Explanation:This problem asks us to examine whether the collection of diagonal matrices within the set of all \( n \times n \) matrices over the real numbers, denoted by \( M_n(\mathbb{R}) \), constitutes a mathematical group when we consider the operation of matrix addition. To evaluate this, we need to consider the definition of a group. A set equipped with an operation forms a group if it satisfies four criteria:1. **Closure**: The set is closed under the operation. For matrix addition, the sum of any two diagonal matrices must also be a diagonal matrix.2. **Associativity**: The operation must be associative, meaning for any three elements \( A, B, \) and \( C \), \( (A + B) + C = A + (B + C) \).3. **Identity Element**: There must be an identity element in the set such that adding it to any element of the set returns the same element. For matrix addition, this is the zero matrix.4. **Inverse Element**: Every element must have an inverse within the set such that the element plus its inverse is the identity element.By systematically proving or disproving these properties, one can determine whether the set of diagonal matrices forms a group under addition.

Name: a.) Explain in your own words what this problem is asking.b.) Explain
Uploaded: 2024-03-20T06:38:58.000Z
Channel: Bartleby
Description: a.) Explain in your own words what this problem is asking.b.) Explain the meaning of any notation used in the problem and in your solution.c.) Describe the mathematical concept(s) that appear to be foundational to this problem.d.) Justified solution