Let `A=[a_("ij")]` be `3xx3` matrix and `B=[b_("ij")]` be `3xx3` matrix such that `b_("ij")` is the sum of the elements of `i^(th)` row of A except `a_("ij")`. If det, `(A)=19`, then the value of det. (B) is ________ .

Answer

38

Explanation

Let `A=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))]`
Given that `|A|=19`.
`B=[(a_(12)+a_(13),a_(11)+a_(13),a_(11)+a_(12)),(a_(22)+a_(23),a_(21)+a_(23),a_(21)+a_(22)),(a_(32)+a_(33),a_(31)+a_(33),a_(31)+a_(32))]`
`|B|=|(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))||(0,1,1),(1,0,1),(1,1,0)|=19xx2=38`