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) AAi`& `j`, `I` is the unit matrix of order 3 and `A^(T)` is the transpose of the matrix `A`
If `|(a_(11)+4,a_(12), a_(3)),(a_(21),a_(22)+4,a_(24)),(a_(31),a_(32),a_(33)+4)|+5lamda|(a_(11)+1,a_(12),a_(13)),(a_(21),a_(22)+1,a_(23)),(a_(31),a_(32),a_(33)+1)|=0` then `lamda=a/b` where `a` and `b` are coprime positive integers then the value of `a+b`is______