Let A be an invertible 3x3 matrix with determinant det(A) = 5. What is the determinant of the matrix 2 * adj(A)?
Answer and explanation
Correct answer: D. 200
- Step 1: For an n x n matrix, det(k M) = k^n det(M). Here n = 3, so det(2 adj(A)) = 2^3 det(adj(A)) = 8 * det(adj(A)).
- Step 2: Recall det(adj(A)) = (det(A))^(n - 1) = 5^(3 - 1) = 5^2 = 25.
- Step 3: Therefore, det(2 adj(A)) = 8 25 = 200.
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