Find the inverse ∣∣∣5364∣∣∣

Question 1 Report

Find the inverse $| \begin{matrix} 5 & 3 \\ 6 & 4 \end{matrix} |$

| \begin{matrix} 2 & - \frac{3}{2} \\ - 3 & - \frac{5}{2} \end{matrix} |

| \begin{matrix} 2 & - \frac{3}{2} \\ - 3 & \frac{5}{2} \end{matrix} |

| \begin{matrix} 2 & \frac{3}{2} \\ - 3 & \frac{5}{2} \end{matrix} |

| \begin{matrix} 2 & \frac{3}{2} \\ - 3 & \frac{5}{2} \end{matrix} |

Answer Details

Let A = $(\begin{matrix} 5 & 3 \\ 6 & 4 \end{matrix})$
Then |A| = $(\begin{matrix} 5 & 3 \\ 6 & 4 \end{matrix})$ = 20 - 18 = 2
Hence A-1 = $\frac{1}{| A |} (\begin{matrix} 4 & - 3 \\ - 6 & 5 \end{matrix})$
= $\frac{1}{2} (\begin{matrix} 4 & - 3 \\ - 6 & 5 \end{matrix})$
= $(\begin{matrix} 4 \times 1 / 2 & - 3 \times 1 / 2 \\ - 6 \times 1 / 2 & 5 \times 1 / 2 \end{matrix})$
= $| \begin{matrix} 2 & - \frac{3}{2} \\ - 3 & \frac{5}{2} \end{matrix} |$

Read lesson note on Modular Arithmetic (WAEC)

Modular Arithmetic

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