If `A=[(3,-4),(1,-1)]` then find tr. `(A^(2012))`.

Explanation

To find the trace of \( A^{2012} \) where \( A = \begin{pmatrix} 3 & -4 \\ 1 & -1 \end{pmatrix} \), we will follow these steps:

### Step 1: Express \( A \) in terms of its Jordan form
To find \( A^{2012} \), we first need to find the eigenvalues of \( A \). The eigenvalues can be found by solving the characteristic polynomial \( \det(A - \lambda I) = 0 \).

\[ A - \lambda I = \begin{pmatrix} 3 - \lambda & -4 \\ 1 & -1 - \lambda \end{pmatrix} \]
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