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The trace of the matrix $A = \begin{bmatrix} 1 & 2 & -1 \\ 0 & 5 & 3 \\ 4 & -2 & 7 \end{bmatrix}$ is:
A$0$
B$7$
C$13$
D$19$
Answer & Solution
Correct answer: C. $13$
Trace $= a_{11} + a_{22} + a_{33} = 1 + 5 + 7 = 13$. The trace is invariant under cyclic permutations: $\operatorname{tr}(AB) = \operatorname{tr}(BA)$, and under similarity: $\operatorname{tr}(P^{-1}AP) = \operatorname{tr}(A)$.
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