Question

If $A=\left[\begin{array}{ccc}0& -1& 2\\ 1& 0& 3\\ -2& -3& 0\end{array}\right]$, then $A+2A^{\prime }$ equals

• A. $A$
• B. $A^{\prime }$
• C. $-A^{\prime }$
• D. $2A$

Answer 1

The correct option is B $A^{\prime }$

$A=\left[\begin{array}{ccc}0& -1& 2\\ 1& 0& 3\\ -2& -3& 0\end{array}\right]$

$\Rightarrow A^{{}^{\prime }}=\left[\begin{array}{ccc}0& 1& -2\\ -1& 0& -3\\ 2& 3& 0\end{array}\right]$

$\Rightarrow {2A}^{{}^{\prime }}=\left[\begin{array}{ccc}0& 2& -4\\ -2& 0& -6\\ 4& 6& 0\end{array}\right]$

$\Rightarrow {A+2A}^{{}^{\prime }}=\left[\begin{array}{ccc}0& 1& -2\\ -1& 0& -3\\ 2& 3& 0\end{array}\right]=A^{{}^{\prime }}$