Question

Find matrix A = (1 3 2 -1) and B = (2 1 - 0 3) find AB and BA​

Answer 1

Answer:

AB  = $\left[\begin{array}{ccc}2&10\\4&-1\end{array}\right]$

BA = $\left[\begin{array}{ccc}4&5\\6&-3\end{array}\right]$

Step-by-step explanation:

A = $\left[\begin{array}{ccc}1&3\\2&-1\end{array}\right]$    B = $\left[\begin{array}{ccc}2&1\\0&3\end{array}\right]$

AB = $\left[\begin{array}{ccc}1&3\\2&-1\end{array}\right]\left[\begin{array}{ccc}2&1\\0&3\end{array}\right]$

= $\left[\begin{array}{ccc}1*2 + 3*0&1*1+3*3\\2*2+ -1*0&2*1+(-1)*3\end{array}\right]$

= $\left[\begin{array}{ccc}2&10\\4&-1\end{array}\right]$

BA = $\left[\begin{array}{ccc}2&1\\0&3\end{array}\right] \left[\begin{array}{ccc}1&3\\2&-1\end{array}\right]$

= $\left[\begin{array}{ccc}2*1+1*2&2*3+ 1 *-1\\0*1+3*2&0*3+3*-1\end{array}\right]$

= $\left[\begin{array}{ccc}4&5\\6&-3\end{array}\right]$