Amit, Biraj and Chirag were given the task of creating a square matrux of order 2.
Below are the matrices created by them. A, B , C are the matrices created by Amit, Biraj and Chirag respectively.
`A=[(1,2),(-1,3)]B=[(4,0),(1,5)]C=[(2,0),(1,-2)]`
If a=4 and b=-2 based on the above information answer the following:
Sum of the matrices A, B and C , `A+(B+C)` is

Options

A. `[(1,6),(2,7)]`
B. `[(6,1),(7,2)]`
C. `[(7,2),(1,6)]`
D. `[(2,1),(7,6)]`

Answer

To solve the problem, we need to find the sum of the matrices A, B, and C, specifically calculating \( A + (B + C) \).

### Step-by-Step Solution:

1. **Identify the matrices**:
- Matrix A:
\[ A = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} \]
- Matrix B:
\[ B = \begin{pmatrix} 4 & 0 \\ 1 & 5 \end{pmatrix} \]
- Matrix C:
\[ C = \begin{pmatrix} 2 & 0 \\ 1 & -2 \end{pmatrix} \]

2. **Calculate \( B + C \)**:
To add matrices B and C, we add the corresponding elements:
\[ B + C = \begin{pmatrix} 4 + 2 & 0 + 0 \\ 1 + 1 & 5 + (-2) \end{pmatrix} \]
Simplifying this gives:
\[ B + C = \begin{pmatrix} 6 & 0 \\ 2 & 3 \end{pmatrix} \]

3. **Calculate \( A + (B + C) \)**:
Now, we add matrix A to the result of \( B + C \):
\[ A + (B + C) = \begin{pmatrix} 1 & 2 \\ -1 & 3 \end{pmatrix} + \begin{pmatrix} 6 & 0 \\ 2 & 3 \end{pmatrix} \]
Again, we add the corresponding elements:
\[ A + (B + C) = \begin{pmatrix} 1 + 6 & 2 + 0 \\ -1 + 2 & 3 + 3 \end{pmatrix} \]
Simplifying this gives:
\[ A + (B + C) = \begin{pmatrix} 7 & 2 \\ 1 & 6 \end{pmatrix} \]

### Final Result:
Thus, the sum \( A + (B + C) \) is:
\[ \begin{pmatrix} 7 & 2 \\ 1 & 6 \end{pmatrix} \]