Question

If A = $\left[\begin{array}{ccc}7&-2\\-1&2\\5&3\end{array}\right]$ and B = $\left[\begin{array}{ccc}-2&-1\\4&2\\-1&0\end{array}\right]$ then find AB' and BA'.

Answer 1

Answer:

$BA'=\left[\begin{array}{ccc}-12&0&-13\\24&0&26\\-7&1&-5\end{array}\right]$

$AB'= \left[\begin{array}{ccc}-12&24&-7\\0&0&1\\-13&26&-5\end{array}\right]$

Step-by-step explanation:

if

$A = \left[\begin{array}{ccc}7&-2\\-1&2\\5&3\end{array}\right]$

$B = \left[\begin{array}{ccc}-2&-1\\4&2\\-1&0\end{array}\right]$

$A^{'} =\left[\begin{array}{ccc}7&-1&5\\-2&2&3\end{array}\right]$

$B^{'} =\left[\begin{array}{ccc}-2&4&-1\\-1&2&0\end{array}\right]$

then to find

$AB'=\left[\begin{array}{ccc}7&-2\\-1&2\\5&3\end{array}\right]_{3\times 2}\times\left[\begin{array}{ccc}-2&4&-1\\-1&2&0\end{array}\right]_{2\times 3}\\\\\\=\left[\begin{array}{ccc}7(-2)+(-2)(-1)&7(4)+(-2)(2)&7(-1)+(-2)(0)\\-1(-2)+2(-1)&(-1)4+-1(-1)&5(-1)+3(0)\\5(-2)+3(-1)&5(4)+3(2)&5(-1)+3(0)\end{array}\right]_{3\times 3}\\\\\\AB'= \left[\begin{array}{ccc}-12&24&-7\\0&0&1\\-13&26&-5\end{array}\right]$

and for BA'

$BA'=\left[\begin{array}{ccc}-2&-1\\4&2\\-1&0\end{array}\right]\times\left[\begin{array}{ccc}7&-1&5\\-2&2&3\end{array}\right]\\\\\\BA'=\left[\begin{array}{ccc}-12&0&-13\\24&0&26\\-7&1&-5\end{array}\right]$