Question

Which of the following is true for a matrix A.

• A. $A=A^T\Rightarrow$ A is skew symmetric
• B. $A=-A^T\Rightarrow$ A is skew symmetric
• C. $A=\overline{A}\Rightarrow$ A is skew symmetric
• D. $A=-A^T\Rightarrow$A is symmetric

Answer 1

The correct option is B

$A=-A^T\Rightarrow$ A is skew symmetric

We have mentioned in the videos that for a square matrix A, if A = $-A^T$then A is said to be a skew symmetric matrix i.e., when we take the transpose of A the new matrix is (-1)x transpose of A.

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

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

Here we can clearly see that in $A^T$ all the corresponding elements of A are multiplied by (-1) i.e., A = - $A^T$ . So this is a skew symmetric matrix. So option (b) is correct.