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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