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If A=[a(i j)] is a square matrix such ...

If `A=[a_(i j)]` is a square matrix such that `a_(i j)=i^2-j^2` , then write whether `A` is symmetric or skew-symmetric.

Text Solution

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Given: `A=[a_(i j)]`is a square matrix such that `a_(i j)=i^2-j^2`
Now, `a_(i i)=i^2-i^2=0` and `a_(j i)=j^2-i^2=-(i^2-j^2)=-a_(ij)`
Hence `a_(ji)=-a_(i j)` for `i !=j` and `a_(ii)=0` for all `i,j`
`implies A^T=-A`
Therefore, A is a skew-symmetric matrix.
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Knowledge Check

  • If A is a square matrix for which a_(ij)=i^(2)-j^(2) , then matrix A is

    A
    unit
    B
    zero
    C
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    D
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    A
    0 for some i
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    D
    1 for all I = 1,2,…,n

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