If `A=[(1,-5,0),(0,7,0),(11,1,9)]` then trace of matrix A is

Options

A. 17
B. 25
C. 3
D. 12

Explanation

To find the trace of the matrix \( A \), we need to follow these steps:

1. **Identify the matrix**: The given matrix \( A \) is
\[ A = \begin{pmatrix} 1 & -5 & 0 \\ 0 & 7 & 0 \\ 11 & 1 & 9 \end{pmatrix} \]

2. **Understand the concept of trace**: The trace of a matrix is defined as the sum of the elements on the main diagonal of the matrix. For a matrix \( A \) of order \( n \times n \), the diagonal elements are \( A_{11}, A_{22}, A_{33}, \ldots, A_{nn} \).

3. **Identify the diagonal elements**: For the matrix \( A \), the diagonal elements are:
- \( A_{11} = 1 \)
- \( A_{22} = 7 \)
- \( A_{33} = 9 \)

4. **Calculate the trace**: Now, we sum these diagonal elements:
\[ \text{Trace}(A) = A_{11} + A_{22} + A_{33} = 1 + 7 + 9 \]

5. **Perform the addition**:
\[ 1 + 7 = 8 \]
\[ 8 + 9 = 17 \]

6. **Conclusion**: Therefore, the trace of matrix \( A \) is \( 17 \).