Question

If $A=⟮\begin{array}{cc}2& 3\\ -9& 5\end{array}⟯-⟮\begin{array}{cc}1& 5\\ 7& -1\end{array}⟯$ , then find the additive inverse of $A$.

Answer 1

$A=⟮\begin{array}{cc}2& 3\\ -9& 5\end{array}⟯-⟮\begin{array}{cc}1& 5\\ 7& -1\end{array}⟯$
$=⟮\begin{array}{cc}2-1& 3-5\\ -9-7& 5+1\end{array}⟯$
$=⟮\begin{array}{cc}1& -2\\ -16& 6\end{array}⟯$
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$\therefore$ Additive inverse of $A=-A$
​​​​​​​$=⟮\begin{array}{cc}-1& 2\\ 16& -6\end{array}⟯$
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