If A is `3xx3` matrix and `|A|=4`, then `|A^(-1)|` is equal to

Options

A. `1/4`
B. `1/16`
C. `4`
D. `2`

Answer

To solve the problem, we need to find the determinant of the inverse of a matrix \( A \) given that \( |A| = 4 \).

### Step-by-step Solution:

1. **Understanding the properties of determinants**:
We know that for any invertible matrix \( A \), the determinant of its inverse is given by the formula:
\[ |A^{-1}| = \frac{1}{|A|} \]

2. **Substituting the given value**:
We are given that \( |A| = 4 \). We can substitute this value into the formula:
\[ |A^{-1}| = \frac{1}{|A|} = \frac{1}{4} \]

3. **Final result**:
Therefore, the determinant of the inverse of matrix \( A \) is:
\[ |A^{-1}| = \frac{1}{4} \]

### Conclusion:
Thus, the value of \( |A^{-1}| \) is \( \frac{1}{4} \).