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Let A=[a(ij)](3 xx 3) be a matrix such ...

Let `A=[a_(ij)]_(3 xx 3)` be a matrix such that `A A^(T) = 4I` and `a_(ij) +2c_(ij)=0` (where `C_(ij)` is the cofactor of `a_(ij)` and I is the unit matrix of order 3). If the determinents are related by
`|(a_(11)+4,a_(12), a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(21)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0`
then `10lambda=`

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Knowledge Check

  • If matrix [(1,2,-1),(3,4,5),(2,6,7)] and its inverse is denoted by A^(-1)=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))] value of a_(32)=

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    B
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    C
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