Matrices

Question

If A is a 3×3 matrix and |A| = 5, then |3A| equals

RankGuru · Accepted Answer

1. **Scalar Property**: For an $n 	imes n$ matrix $A$ and a scalar $k$, the property of determinants is $|kA| = k^n |A|$.
2. **Identify Values**: Given order $n = 3$, scalar $k = 3$, and determinant $|A| = 5$.
3. **Calculate**:
   - $|3A| = 3^3 	imes |A|$
   - $|3A| = 27 	imes 5$
4. **Result**: $135$.
- Reason: Multiplying a matrix by a constant multiplies every row, and since there are 3 rows, the constant factor comes out as $k \cdot k \cdot k$.

Rank Guru

Matrices

Select the correct option:

Solution

🔒 Solution Hidden from View

More matrices Practice Questions

If A = [[1, 2], [3, 4]] and B = [[2, 0], [1, 3]], then AB equals

The transpose of matrix A = [[1, 2, 3], [4, 5, 6]] is

About This Question

Solution