Determinants

Question

If A and B are square matrices of order 3 such that |A| = 2 and |B| = 3, then |AB| equals

RankGuru · Accepted Answer

1. **Determinant of Product**: A fundamental property of determinants states that for any two square matrices $A$ and $B$, $|AB| = |A| 	imes |B|$.
2. **Application**: 
   - $|AB| = (2) 	imes (3) = 6$.
3. **Result**: The determinant of the product is 6. Note that this property holds regardless of the matrix size of order $n$.

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