A is a 5xp matrix, B is a 2xq matrix, AB works out to be a 5?4 matrix. Write the value of p and q

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$$\begin{gathered} \mathrm{We} \mathrm{know} \mathrm{that} \mathrm{for} \mathrm{multuplication} \mathrm{AB} \mathrm{to} \mathrm{exist} \\ \mathrm{Column} \mathrm{of} \mathrm{A}=\mathrm{Row} \mathrm{of} \mathrm{B} \\ \mathrm{And} \\ \mathrm{Order} \mathrm{of} \mathrm{AB}=\left(\mathrm{Row} \mathrm{of} \mathrm{A}\right)\times \left(\mathrm{Column} \mathrm{of} \mathrm{B}\right) \\ \mathrm{We} \mathrm{we} \mathrm{have} \\ \mathrm{A}\to 5\times \mathrm{p} \mathrm{and} \mathrm{B}\to 2\times \mathrm{q} \\ \mathrm{Hence} \\ \mathrm{p}=2 \\ \mathrm{Order} \mathrm{of} \mathrm{AB}=\left(\mathrm{Row} \mathrm{of} \mathrm{A}\right)\times \left(\mathrm{Column} \mathrm{of} \mathrm{B}\right)=5\times \mathrm{q} \\ \mathrm{According} \mathrm{to} \mathrm{question} \\ 5\times \mathrm{q} \mathrm{is} 5\times 4 \\ \mathrm{Hence} \mathrm{q}=4 \end{gathered}$$

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