====== Question 11, Exercise 2.2 ======
Solutions of Question 11 of Exercise 2.2 of Unit 02: Matrices and Determinants. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. 

=====Question 11=====
If $A=\left[a_{i j}\right]$ is a matrix of order $3 \times 3$ and $a_{i j}=i^{2}-j^{2}$. Check whether $A$ is symmetric or skew-symmetric.

** Solution. **

A matrix $A=\left[a_{i j}\right]$ is symmetric if $a_{ij}=a+{ji}$ and skew-symmetric if $a_{ij}=-a_{ji}$.

Given $a_{i j}=i^{2}-j^{2}$, then
\begin{align}
a_{ji} & = j^2 -i^2 \\
&= - (i^2 -j^2) \\
&= - a_{ij}
\end{align}
This gives $a_{ij}=-a_{ji}$, hence given matrix is skew-symmetric.


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