Question

If $A=\left[\begin{array}{cc}3& -4\\ 2& 8\end{array}\right]\text{and}B=\left[\begin{array}{cc}-1& -6\\ 2& 0\end{array}\right]$
Is (A + B)' = A' .+ B'

• A. Yes
• B. No

Answer 1

The correct option is A

Yes

If $A=\left[\begin{array}{cc}3& -4\\ 2& 8\end{array}\right]\text{and}B=\left[\begin{array}{cc}-1& -6\\ 2& 0\end{array}\right]$

$A+B=\left[\begin{array}{cc}2& -10\\ 4& 8\end{array}\right]$

$(A+B{)}^{\prime }=\left[\begin{array}{cc}2& 4\\ -10& 8\end{array}\right]$ .....(i)

$A^{\prime }=\left[\begin{array}{cc}3& 2\\ -4& 8\end{array}\right]B^{\prime }=\left[\begin{array}{cc}-1& 2\\ -6& 0\end{array}\right]$

$A^{\prime }+B^{\prime }=\left[\begin{array}{cc}2& 4\\ -10& 8\end{array}\right]$ ....(ii)
From (i) and (ii) we can see that (A+B)'=A'+B'