A matrix P has an inverse P\(^{-1}\) = \(\begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix}\). Find P
Let \( A = \begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix} \) (given as \( P^{-1} \)).
Determinant of \( A \) = \( (1)(1) - (-3)(0) = 1 \).
Inverse of \( A \) is \( \frac{1}{1} \begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix} \), which is exactly \( P \).
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