For a 3×3 matrix A, if |A| = −2, then ||A|·adj A| equals:
For a 3×3 matrix A, if |A| = −2, then ||A|·adj A| equals:
- A. −8
- B. 8
- C. −32
- D. 32
Answer: D) 32
Explanation: ||A|A| = |A|³|A|? |adj A| = |A|² = 4. Then | |A|·adj A | = |A|³ × |adj A| = (−2)³ × 4 = −8 × 4 = −32. We recompute: |kA| = kⁿ|A|. Here k=|A|=-2, matrix is adj A (size 3). So | |A| adj A| = |A|³ |adj A| = (−2)³ × 4 = −32. Option 2 is −32.
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