Matrices and Determinants
Properties of Determinants
Premium Question
Grade 12
Question:
If $A$ is a $3 \times 3$ matrix with $|A| = 3$, then $|A^T|$ equals:
(1) $-3$
(2) $3$
(3) $9$
(4) $\frac{1}{3}$
Step-by-Step Solution
Key Concept: Recall the basic property relating the determinant of a matrix to the determinant of its transpose: $|A^T| = |A|$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)