Question

Given A = 2x2 Matrix, B = 2x2 Matrix
Is there a shortcut for finding the first column of AxB?

Answer 1

\[A = \left[\begin{matrix}a & b \\ c & d\end{matrix}\right] B = \left[\begin{matrix}e & f \\ g & h\end{matrix}\right]\]

Answer 2

\[AB = \left[\begin{matrix}ae+bg & af+gh \\ ce+dg & cf+dh\end{matrix}\right]\]

Answer 3

First column: \[\left[\begin{matrix}ae+bg \\ ce+dg \end{matrix}\right]\]

Answer 4

Which is
A * (first row of B)

Answer 5

First row:
\[\left[\begin{matrix}ae+bg & af+gh \end{matrix}\right]\]

which is First row of A * B