Question

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

• A. $A$
• B. $-A^T$
• C. $A^T$
• D. $2A^2$

Answer 1

Answer: (C)

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