matrix properties

Question

The trace of a square matrix A is defined as the sum of its diagonal elements. If A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]], then tr(A) equals

RankGuru · Accepted Answer

1. **Identify Diagonals**: In a square matrix, the diagonal elements are those where the row index equals the column index ($a_{11}, a_{22}, \dots$).
2. **Identify Elements in A**: The main diagonal elements are $1, 5,$ and $9$.
3. **Calculation**:
   - $tr(A) = 1 + 5 + 9 = 15$.
4. **Result**: The trace is 15.

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