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WAEC 2020 · Paper 2 · Q2

Given that P=(3456)P = \begin{pmatrix} 3 & 4 \\ 5 & 6 \end{pmatrix} and Q=(−25−31)Q = \begin{pmatrix} -2 & 5 \\ -3 & 1 \end{pmatrix}, find PQ−1PQ^{-1}, where Q−1Q^{-1} is the inverse of QQ.

    Worked solution (try it first)
    1. ∣Q∣=(−2)(1)−(5)(−3)=−2+15=13|Q| = (-2)(1) - (5)(-3) = -2 + 15 = 13.
    2. Q−1=113(1−53−2)Q^{-1} = \frac{1}{13}\begin{pmatrix} 1 & -5 \\ 3 & -2 \end{pmatrix}.
    3. PQ−1=113(3+12−15−85+18−25−12)PQ^{-1} = \frac{1}{13}\begin{pmatrix} 3 + 12 & -15 - 8 \\ 5 + 18 & -25 - 12 \end{pmatrix}
      =113(15−2323−37)= \frac{1}{13}\begin{pmatrix} 15 & -23 \\ 23 & -37 \end{pmatrix}.

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