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. **Definition of Matrix Equality**: Two matrices \( A \) and \( B \) of the same order (i.e., they have the same number of rows and columns) are said to be equal if every corresponding element in both matrices is equal.

2. **Element Comparison**: Suppose we have two matrices:
\[ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}, \quad B = \begin{pmatrix} b_{11} & b_{12} \\ b_{21} & b_{22} \end{pmatrix} \]
For these matrices to be equal, the following conditions must hold:
\[ a_{11} = b_{11}, \quad a_{12} = b_{12}, \quad a_{21} = b_{21}, \quad a_{22} = b_{22} \]

3. **Conclusion**: Therefore, we conclude that two matrices \( A \) and \( B \) are equal if and only if all corresponding elements are equal.

### Final Answer:
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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