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Let A=[a("ij")](3xx3) be a matrix such t...

Let `A=[a_("ij")]_(3xx3)` 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.
`|(a_(11)+4,a_(12),a_(13)),(a_(21),a_(22)+4,a_(23)),(a_(31),a_(32),a_(33)+4)|+5 lambda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0`
then the value of `lambda` is

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