A matrix P has an inverse P\(^{-1}\) = \(\begin{pmatrix} 1 & -3 \\ 0 & 1 \end{pmatrix}\). Find P
A
\(\begin{pmatrix} -1 & 3 \\ 0 & -1 \end{pmatrix}\)
B
\(\begin{pmatrix} 1 & 3 \\ 0 & -1 \end{pmatrix}\)
C
\(\begin{pmatrix} 1 & -3 \\ 0 & -1 \end{pmatrix}\)
D
\(\begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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 \( P \).
Source: Myschool Past Questions Archive (Record #76305)