If `[(a+b,2),(5,b)]=[(6,2),(5,2)]`, then the value of a is :

Options

A. 4
B. 2
C. 0
D. 1

Answer

To solve the equation given by the matrices \([(a+b, 2), (5, b)] = [(6, 2), (5, 2)]\), we will equate the corresponding elements of the matrices.

### Step-by-Step Solution:

1. **Identify the Elements of the Matrices:**
We have two matrices:
\[ \text{Matrix 1: } \begin{pmatrix} a+b & 2 \\ 5 & b \end{pmatrix} \]
\[ \text{Matrix 2: } \begin{pmatrix} 6 & 2 \\ 5 & 2 \end{pmatrix} \]

2. **Set Up the Equations:**
Since the matrices are equal, we can equate their corresponding elements:
- From the first row, first column: \(a + b = 6\) (1)
- From the first row, second column: \(2 = 2\) (This is always true)
- From the second row, first column: \(5 = 5\) (This is also always true)
- From the second row, second column: \(b = 2\) (2)

3. **Substitute the Value of \(b\):**
From equation (2), we have \(b = 2\). We can substitute this value into equation (1):
\[ a + 2 = 6 \]

4. **Solve for \(a\):**
To find \(a\), we rearrange the equation:
\[ a = 6 - 2 \]
\[ a = 4 \]

5. **Conclusion:**
The value of \(a\) is \(4\).

### Final Answer:
The value of \(a\) is \(4\).