Row by column rule for 2x2 multiplication for JEE

Formula

\[\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}e&f\\g&h\end{bmatrix}=\begin{bmatrix}ae+bg&af+bh\\ce+dg&cf+dh\end{bmatrix}\]

Variables: \(a,b,c,d,e,f,g,h\): matrix entries.

Conditions: Both matrices are of order \(2\times 2\).

Direct computation of matrix products in JEE problems.