If `A=[a_(i j)]` is a square matrix of even order such that `a_(i j)=i^2-j^2` , then `A` is a skew-symmetric matrix and `|A|=0` (b) `A` is symmetric matrix and `|A|` is a square (c) `A` is symmetric matrix and `|A|=0` (d) none of these

Explanation

Given:`A=[a_(i j)]`
is a square matrix of
even order such that `a_(i j)=i^2-j^2`

Then

`a_(ii)=i^2-i^2=0`,

`a_(ji)=j^2-i^2=-(i^2-j^2)=-a_(ij)`

Hence, `a_(ji)=-a_(ij)` for all `i!=j` and `a_(ii)=0` for all `i,j`

`implies A^T=-A`

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