Question

If A is a square matric $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then A - A^T ­ is symmetric.

• A. True
• B. False

Answer 1

The correct option is B

False

Here A$=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ $A^T$will be $\left[\begin{array}{ccc}1& 4& 7\\ 2& 5& 8\\ 3& 6& 9\end{array}\right]$ $A-A^T$ will be obtained by subtractions of corresponding elements of $A^T$ from A. So, $A-A^T$ $=\left[\begin{array}{ccc}(1-1)& (2-4)& (3-7)\\ (4-2)& (5-5)& (6-8)\\ (7-3)& (8-6)& (9-9)\end{array}\right]$ $B=\left[\begin{array}{ccc}0& -2& -4\\ 2& 0& -2\\ 4& 2& 0\end{array}\right]$