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Find the inverse of  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)

Further Mathematics
WAEC 2021

Find the inverse of  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\)

  • A.  \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)
  • B.  \(\begin{pmatrix} 1 & -1 \\ 1.5 & -2 \end{pmatrix}\)
  • C.  \(\begin{pmatrix} -2 & 1 \\ 1.5 & 1 \end{pmatrix}\)
  • D. \(\begin{pmatrix} -2 & -1 \\ 1.5 & 1 \end{pmatrix}\)
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Correct Answer: Option A
Explanation

Let A =  \(\begin{pmatrix} 4 & 2 \\ -3 & -2 \end{pmatrix}\);

|A| = -8 - (-6) = -8 + 6

|A| = -2

A\(^{-1}\) = \(\frac{1}{-2}\) =  \(\begin{pmatrix} -2 & 2- \\ 3 & 4 \end{pmatrix}\)

= \(\begin{pmatrix} 1 & 1 \\ -1.5 & -2 \end{pmatrix}\)

 


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