Two matrices of some order are said to be equal if the….of the matrices are equal.

Options

A. Corresponding elements
B. Diagonal elements
C. Only non-diagonal elements
D. None of the above

Answer

To determine when two matrices are equal, we need to analyze the conditions under which they can be considered equal. Here’s a step-by-step solution:

### Step 1: Understand the Definition of Matrix Equality
Two matrices are said to be equal if they have the same dimensions and all their corresponding elements are equal.

### Step 2: Identify the Elements of the Matrices
Let’s consider two matrices \( A \) and \( B \) of the same order. For example, if both matrices are of order \( 2 \times 2 \), then:
- Matrix \( A \) can be represented as:
\[ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix} \]
- Matrix \( B \) can be represented as:
\[ B = \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix} \]

### Step 3: Set the Corresponding Elements Equal
For matrices \( A \) and \( B \) to be equal, the following conditions must hold:
- \( a_{11} = b_{11} \)
- \( a_{12} = b_{12} \)
- \( a_{21} = b_{21} \)
- \( a_{22} = b_{22} \)

### Step 4: Conclude the Condition for Equality
Thus, we conclude that two matrices are equal if all corresponding elements are equal.

### Final Answer
Two matrices of some order are said to be equal if the **corresponding elements** of the matrices are equal.

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