Question

Let $A=[a_{ij}{]}_{n\times n}$ where $a_{ij}=i^2-j^2$. Show that $A$ is skew symmetric matrix.

Answer 1

Given, $A=[a_{ij}{]}_{n\times n}$ where $a_{ij}=i^2-j^2$.

Now, $a_{ji}=j^2-i^2=-(i^2-j^2)=-a_{ij}$, $\forall i,j$.

Also $a_{ii}=0$, $\forall i$.

So $A^T=-A$. [According to the definition of symmetric matrix]