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If A is a square matrix of order n with |A| = 9 and |adj A| = 3¹⁶, find the number of elements in A.
- 81
- 27
- 9
- 3
Correct answer: 81
Solution
From |adj A| = |A|^(n-1): 3¹⁶ = 9^(n-1) = 3^(2(n-1)), so 2(n-1)=16, n=9. A 9x9 matrix has 9² = 81 elements.
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