Answer :

Given: A = [aij] is a square matrix such that aij = i2 – j2

Suppose A is a 2 × 2 square matrix i.e.



Here,


aij = i2 – j2


So, a12 = (1)2 – (2)2 = 1 – 4 = - 3


and a21 = (2)2 – (1)2 = 4 – 1 = 3


For diagonal elements, i = j, we have


a11 = (1)2 – (1)2 = 0


and a22 = (2)2 – (2)2 = 0


So, Matrix A becomes



Now, we have to check A is symmetric or skew – symmetric.


We know that, if a matrix is symmetric then AT = A


and if a matrix is skew – symmetric then AT = -A


So, firstly we find the AT



So,




AT = - A


A is a skew – symmetric matrix.


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