If |adj(A)|= 11 and A is a square matrix of order 2then find the value of |A|

Answer

To solve the problem, we start with the given information and apply the relevant mathematical properties.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We have that \(|\text{adj}(A)| = 11\) and \(A\) is a square matrix of order 2.

2. **Using the Property of Determinants**:
The determinant of the adjoint of a matrix \(A\) is given by the formula:
\[ |\text{adj}(A)| = |\text{det}(A)|^{n-1} \]
where \(n\) is the order of the matrix. Since \(A\) is a \(2 \times 2\) matrix, we have \(n = 2\).

3. **Substituting the Values**:
Now, substituting \(n = 2\) into the formula, we get:
\[ |\text{adj}(A)| = |\text{det}(A)|^{2-1} = |\text{det}(A)|^{1} \]
This simplifies to:
\[ |\text{adj}(A)| = |\text{det}(A)| \]

4. **Setting Up the Equation**:
From the problem, we know that \(|\text{adj}(A)| = 11\). Therefore, we can write:
\[ |\text{det}(A)| = 11 \]

5. **Conclusion**:
Thus, the value of \(|A|\) (the determinant of matrix \(A\)) is:
\[ |A| = 11 \]

### Final Answer:
\[ |A| = 11 \]