If `A=[{:(6,0),(p,q):}]` is a scalar matrix then the value of p and q are

Options

A. 6 and 0
B. 0 and 6
C. 5 and 6
D. 0 and 1

Answer

To solve the problem, we need to determine the values of \( p \) and \( q \) in the scalar matrix \( A = \begin{pmatrix} 6 & 0 \\ p & q \end{pmatrix} \).

### Step-by-Step Solution:

1. **Understanding Scalar Matrix**: A scalar matrix is a special type of diagonal matrix where all the diagonal elements are equal, and all off-diagonal elements are zero.

2. **Identifying the Matrix Elements**: In our matrix \( A \), we have:
\[ A = \begin{pmatrix} 6 & 0 \\ p & q \end{pmatrix} \]
Here, the diagonal elements are \( 6 \) (top left) and \( q \) (bottom right), while the off-diagonal elements are \( 0 \) (top right) and \( p \) (bottom left).

3. **Setting Up the Equations**: For \( A \) to be a scalar matrix, the diagonal elements must be equal:
\[ 6 = q \]
Additionally, since all off-diagonal elements must be zero, we have:
\[ p = 0 \]

4. **Finding Values of \( p \) and \( q \)**: From the equations derived:
- From \( 6 = q \), we find \( q = 6 \).
- From \( p = 0 \), we find \( p = 0 \).

5. **Final Values**: Thus, the values of \( p \) and \( q \) are:
\[ p = 0, \quad q = 6 \]

### Summary of the Solution:
The values of \( p \) and \( q \) are:
- \( p = 0 \)
- \( q = 6 \)