If A is a non singular square matrix of order 3 such that `A^(2)=3A`, then the value of |A| is

Options

A. `-3`
B. 3
C. 9
D. 27

Answer

To solve the problem, we need to find the determinant of the matrix \( A \) given that \( A^2 = 3A \) and \( A \) is a non-singular square matrix of order 3.

### Step-by-Step Solution:

1. **Given the equation**: We start with the equation \( A^2 = 3A \).

2. **Rearranging the equation**: We can rearrange this equation as:
\[ A^2 - 3A = 0 \]
This can be factored as:
\[ A(A - 3I) = 0 \]
where \( I \) is the identity matrix of order 3.

3. **Using the property of determinants**: Since \( A \) is a non-singular matrix, we know that \( |A| \neq 0 \). Therefore, we can conclude that:
\[ A - 3I = 0 \]
This implies that \( A = 3I \).

4. **Finding the determinant**: We can now find the determinant of \( A \):
\[ |A| = |3I| = 3^3 = 27 \]

5. **Conclusion**: Thus, the value of \( |A| \) is:
\[ |A| = 27 \]

### Final Answer:
The value of \( |A| \) is \( 27 \).