Statement 1: If A=([a(i j)])(nxxn) is su...

Statement 1: If `A=([a_(i j)])_(nxxn)` is such that `( a )_(i j)=a_(j i),AAi ,ja n dA^2=O ,` then matrix `A` null matrix. Statement 2: `|A|=0.`

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Since `a_("iJ")=bar(a)_("ji")`, let `A=[(d_(1),z_(1),z_(2)),(bar(z)_(1),d_(2),z_(3)),(bar(z)_(2),bar(z)_(3),d_(3))]`, where `d_(1), d_(2), d_(3) in R`
Given, `A^(2)=O`
`implies [(d_(1),z_(1),z_(2)),(bar(z)_(1),d_(2),z_(3)),(bar(z)_(2),bar(z)_(3),d_(3))][(d_(1),z_(1),z_(2)),(bar(z)_(1),d_(2),z_(3)),(bar(z)_(2),bar(z)_(3),d_(3))]`
`[(d_(1)^(2)+|z_(1)|^(2)+|z_(2)|^(2),d_(1)z_(1)+d_(2)z_(1)+z_(2)bar(z)_(3),d_(1)z_(2)+z_(1)z_(3)+z_(2)d_(3)),(d_(1)bar(z)_(1)+d_(2)bar(z)_(1)+z_(3)bar(z)_(2),d_(2)^(2)+|z_(1)|^(2)+|z_(3)|^(2),bar(z)_(1)z_(2)+d_(2)z_(3)+z_(3)d_(3)),(d_(1)bar(z)_(2)+bar(z)_(3)bar(z)_(1)+d_(3)bar(z)_(2),z_(1) bar(z)_(2)+d_(2)bar(z)_(3)+d_(3)bar(z)_(3),d_(3)^(2)+|z_(1)|^(2)+|z_(2)|^(2))]`

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