Let A `2xx2` matrix A has determinant Find |adj(A)| if determinant of A Is 9

Explanation

To find the determinant of the adjoint of a 2x2 matrix \( A \) given that the determinant of \( A \) is 9, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between the determinant of a matrix and its adjoint**:
The determinant of the adjoint of a matrix \( A \) can be calculated using the formula:
\[ |\text{adj}(A)| = |A|^{n-1} \]
where \( |A| \) is the determinant of matrix \( A \) and \( n \) is the order of the matrix.

2. **Identify the order of the matrix**:
Since \( A \) is a 2x2 matrix, the order \( n \) is 2.

3. **Substitute the values into the formula**:
Given that \( |A| = 9 \) and \( n = 2 \), we can substitute these values into the formula:
\[ |\text{adj}(A)| = |A|^{2-1} = |A|^{1} \]

4. **Calculate the determinant of the adjoint**:
Now substituting the value of \( |A| \):
\[ |\text{adj}(A)| = 9^{1} = 9 \]

### Final Answer:
Thus, the determinant of the adjoint of matrix \( A \) is \( 9 \).

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