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JAMB 2013 · UTME · Q23

Find the inverse of (5364)\begin{pmatrix} 5 & 3 \\ 6 & 4 \end{pmatrix}.

Worked solution (try it first)
  1. The determinant is 5×4−3×6=20−18=25 \times 4 - 3 \times 6 = 20 - 18 = 2.
  2. Swap the two diagonal entries (5 and 4) and change the signs of the other two: (4−3−65)\begin{pmatrix} 4 & -3 \\ -6 & 5 \end{pmatrix}.
  3. Divide every entry by 2: (2−32−352)\begin{pmatrix} 2 & -\frac32 \\ -3 & \frac52 \end{pmatrix}, option D.

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