Q. 195.0( 2 Votes )

# If A = [aij<

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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