If A is any square matrix such that `A= [ ( 2, 3) , (5,8)]` then find `A+I`

Explanation

To find \( A + I \) where \( A \) is the given matrix and \( I \) is the identity matrix, we can follow these steps:

### Step 1: Identify the matrix A
Given the matrix \( A \):
\[ A = \begin{pmatrix} 2 & 3 \\ 5 & 8 \end{pmatrix} \]

### Step 2: Identify the identity matrix I
The identity matrix \( I \) of order \( 2 \times 2 \) is:
\[ I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \]

### Step 3: Add the matrices A and I
Now, we will add the corresponding elements of matrices \( A \) and \( I \):
\[ A + I = \begin{pmatrix} 2 & 3 \\ 5 & 8 \end{pmatrix} + \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} \]

Calculating the sum:
- For the element at (1,1): \( 2 + 1 = 3 \)
- For the element at (1,2): \( 3 + 0 = 3 \)
- For the element at (2,1): \( 5 + 0 = 5 \)
- For the element at (2,2): \( 8 + 1 = 9 \)

Thus, we have:
\[ A + I = \begin{pmatrix} 3 & 3 \\ 5 & 9 \end{pmatrix} \]

### Final Result
The result of \( A + I \) is:
\[ A + I = \begin{pmatrix} 3 & 3 \\ 5 & 9 \end{pmatrix} \]

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