Question

Given a square matrix $A=\left[a_g\right]$, where $a_g={\hat{i}}^2-{\hat{j}}^2$. Then matrix A is a unit matrix or null matrix or a symmetric matrix a skew symmetric matrix. Select with a reason.

Answer 1

Let's design a $2\times 2$ metrics

$a_{11}=1^2-1^2=0$

$a_{12}=1^2-2^2=-3$

$a_{21}=2^2-1^2=3$

$a_{22}=2^2-2^2=0$

$\therefore A=\left[\begin{array}{cc}0& -3\\ 3& 0\end{array}\right]$, then $A^T=\left[\begin{array}{cc}0& 3\\ -3& 0\end{array}\right]$

Clearly matrices A is a skew symmetric matrix.