Answer:
The products of AB and BA is given by
AB=[tex]\left[\begin{array}{cc}21&-6\\ 9&3\end{array}\right][/tex]
BA=[tex]\left[\begin{array}{cc}9&-1\\-18&15\end{array}\right][/tex]
Step-by-step explanation:
Given the matrices A=[tex]\left[\begin{array}{cc}6&-5\\-3&-4\end{array}\right][/tex] and
B=[tex]\left[\begin{array}{cc}1&-1\\-3&0\end{array}\right][/tex]
To find the product AB and BA
AB=[tex]\left[\begin{array}{cc}6&-5\\-3&-4\end{array}\right] \left[\begin{array}{cc}1 & -1\\-3 &0\end{array}\right][/tex]
[tex]=\left[\begin{array}{cc}6+15& -6+0\\-3+12&3-0\end{array}\right][/tex]
Therefore the product of AB is
AB=[tex]\left[\begin{array}{cc}21&-6\\ 9&3\end{array}\right][/tex]
BA=[tex]\left[\begin{array}{cc}1&-1\\-3&0\end{array}\right][/tex] [tex]\left[\begin{array}{cc}6&-5\\-3&-4\end{array}\right][/tex]
[tex]=\left[\begin{array}{cc}6+3& -5+4\\-18+0&15+0\end{array}\right][/tex]
Therefore the product of BA is
BA=[tex]\left[\begin{array}{cc}9&-1\\-18&15\end{array}\right][/tex]
The products of AB and BA is given by
AB=[tex]\left[\begin{array}{cc}21&-6\\ 9&3\end{array}\right][/tex]
BA=[tex]\left[\begin{array}{cc}9&-1\\-18&15\end{array}\right][/tex]
