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A matrix P has an inverse P\(^{-1}\) = \(\begin{pmatrix} 1 & -3 \\ 0 &...

Mathematics
JAMB 2003

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. \(\begin{pmatrix} 1 & 3 \\ 0 & 1 \end{pmatrix}\)
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Correct Answer: Option D
Explanation

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 \( P \).

There is an explanation video available below.


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Explanation Video

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