Find the inverse of the diagonal matrix D = diag(2, -3, 5).
Answer and explanation
Correct answer: A. diag(1/2, -1/3, 1/5)
- Step 1: For any diagonal matrix with non-zero diagonal entries, D^(-1) is obtained by taking the reciprocal of each diagonal entry.
- Step 2: D^(-1) = diag(1/2, -1/3, 1/5).
Why not the others: The remaining values (diag(2, -3, 5), diag(-2, 3, -5), diag(1/4, 1/9, 1/25)) result from evaluating the determinant instead of the trace, adding off-diagonal entries, or sign errors.
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