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the square matrix A=[a(ij)](mxxn) given ...

the square matrix `A=[a_(ij)]_(mxxn)` given by`a_(ij)=(i-j)^(n),` show that A is symmetic and skew-sysmmetic matrices according as n is even or odd, repectively.

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`therefore " "a_(ij)=(i-j)^(n)=(-1)^(n) (j-i)^(n)`
`=(-1)^(n) a_(ij)={{:(a_(ji)", n is even interger"),(-a_(ji)", n is odd integer"):}`
Hence , A is symmetric if n is even ana skew-symmetric if n is odd integer.
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