Two matrices of same order are said to be equal if the ………… of the two 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 of the same order are equal, we need to follow these steps:

### Step-by-Step Solution:

1. **Understanding Matrix Order**:
- The order of a matrix is defined by the number of rows and columns it contains. For example, a matrix with 2 rows and 2 columns is said to be of order 2x2.

2. **Defining Two Matrices**:
- Let’s consider two matrices, A and B, both of the same order (for instance, both are 2x2 matrices).
- 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:
\[ B = \begin{pmatrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{pmatrix} \]

3. **Condition for Equality**:
- For two matrices A and B to be equal, all corresponding elements of the matrices must be equal. This means:
- \( A_{11} = B_{11} \)
- \( A_{12} = B_{12} \)
- \( A_{21} = B_{21} \)
- \( A_{22} = B_{22} \)

4. **Conclusion**:
- Therefore, two matrices of the same order are equal if and only if all their corresponding elements are equal.

### Final Statement:
Two matrices of the same order are said to be equal if the **corresponding elements** of the two matrices are equal.

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