Question

If A = ${\displaystyle \left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]\text{and}\text{B}=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]}$, fin A(BA)

Answer 1

A = ${\displaystyle \left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]}$

B = ${\displaystyle \left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]}$

BA = ${\displaystyle \left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]\times \left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}2+2& 4+1\\ 1+4& 2+2\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}4& 5\\ 5& 4\end{array}\right]}$

A(BA) = ${\displaystyle \left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right]\times \left[\begin{array}{cc}4& 5\\ 5& 4\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}4+10& 5+8\\ 8+5& 10+4\end{array}\right]}$

= ${\displaystyle \left[\begin{array}{cc}14& 13\\ 13& 14\end{array}\right]}$.