If a number of rows and that of columns of a matrix are equal and the matrix contains 36 elements , then the order of the matrix is ________.

Options

A. `3xx3`
B. `4xx4`
C. `8xx8`
D. `6xx6`

Answer

To find the order of the matrix given that the number of rows and columns are equal and the matrix contains 36 elements, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**: Let the number of rows be denoted as \( r \) and the number of columns as \( c \). Since the number of rows and columns are equal, we can say \( r = c \).

2. **Set Up the Equation**: The total number of elements in a matrix is given by the product of the number of rows and the number of columns. Therefore, we can write the equation:
\[ r \times c = 36 \]
Since \( r = c \), we can substitute \( c \) with \( r \):
\[ r \times r = 36 \]
This simplifies to:
\[ r^2 = 36 \]

3. **Solve for \( r \)**: To find \( r \), we take the square root of both sides:
\[ r = \sqrt{36} \]
This gives us:
\[ r = 6 \quad (\text{since the number of rows cannot be negative}) \]

4. **Determine the Order of the Matrix**: Since \( r = c = 6 \), the order of the matrix is:
\[ r \times c = 6 \times 6 \]
Therefore, the order of the matrix is \( 6 \times 6 \).

### Final Answer:
The order of the matrix is \( 6 \times 6 \).

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