Question

If A = $\left[\begin{array}{ccc}2&-4\\-5&3\end{array}\right]$ then find A + A' and AA'

Answer 1

Answer:

$A + A^{'}=\left[\begin{array}{ccc}4&-9\\-9&6\end{array}\right]$

$A.A^{'}=\left[\begin{array}{ccc}20&-22\\-22&34\end{array}\right]$

Step-by-step explanation:

If

$A =\left[\begin{array}{ccc}2&-4\\-5&3\end{array}\right]$

 then

$A^{'} =\left[\begin{array}{ccc}2&-5\\-4&3\end{array}\right]$

so to find

$A + A^{'}=\left[\begin{array}{ccc}2&-4\\-5&3\end{array}\right]+\left[\begin{array}{ccc}2&-5\\-4&3\end{array}\right]\\\\\\\=\left[\begin{array}{ccc}2+2&-4-5\\-5-4&3+3\end{array}\right]$

$A +A^{'}=\left[\begin{array}{ccc}4&-9\\-9&6\end{array}\right]$

and for

$A.A^{'}=\left[\begin{array}{ccc}2&-4\\-5&3\end{array}\right]\times\left[\begin{array}{ccc}2&-5\\-4&3\end{array}\right]\\\\\\A.A^{'}=\left[\begin{array}{ccc}20&-22\\-22&34\end{array}\right]$