If `A` is a matrix of order `3xx3`, then `|3A|` is equal to………

Explanation

To solve the problem of finding \(|3A|\) where \(A\) is a \(3 \times 3\) matrix, we can use the property of determinants related to scalar multiplication of matrices. Here’s the step-by-step solution:

### Step 1: Understand the property of determinants
For any \(n \times n\) matrix \(A\) and a scalar \(k\), the determinant of the matrix \(kA\) is given by the formula:
\[ |kA| = k^n |A| \]
where \(n\) is the order of the matrix.

### Step 2: Identify the order of the matrix
In this case, the matrix \(A\) is of order \(3 \times 3\), which means \(n = 3\).

### Step 3: Substitute the values into the formula
We need to find \(|3A|\). Using the property identified in Step 1, we substitute \(k = 3\) and \(n = 3\):
\[ |3A| = 3^3 |A| \]

### Step 4: Calculate \(3^3\)
Now, calculate \(3^3\):
\[ 3^3 = 27 \]

### Step 5: Write the final result
Thus, we can express \(|3A|\) as:
\[ |3A| = 27 |A| \]

### Conclusion
The determinant \(|3A|\) is equal to \(27\) times the determinant of \(A\).