[A=[[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]]" then trace "],[" of "A" is "]

If matrix A=[[1, 0, -1], [3, 4, 5], [0, 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)]], then the value of a_(23) =

If A = [{:(3," "1,-1),(2,-2," "0),(1," "2,-1):}] "and"" "A^(-1)=[(a_(11),a_(12),a_(13)),(a_(21),a_(22),a_(23)),(a_(31),a_(32),a_(33))] then the value of a_(23) is

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and a_(ij) denote the cofactor of element A_(ij) , then a_(11)A_(11)+a_(12)A_(12)+a_(13)A_(13)=

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by A. a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) B. a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) C. a_(21)A_(11) + a_(22)A_(12) + a_(23)A_(13) D. a_(11)A_(11) + a_(21)A_(21) + a_(31)A_(31)

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by A. a_(11)A_(31)+a_(12)A_(32)+a_(13)A_(33) B. a_(11)A_(11)+a_(12)A_(21)+a_(13)A_(31) C. a_(21)A_(11) + a_(22)A_(12) + a_(23)A_(13) D. a_(11)A_(11) + a_(21)A_(21) + a_(31)A_(31)

If A=[[a_(11), a_(12), a_(13)], [a_(21), a_(22), a_(23)], [a_(31), a_(32), a_(33)]] and A_(ij) denote the cofactor of element a_(ij) , then a_(11)A_(21)+a_(12)A_(22)+a_(13)A_(23)=

If Delta=|[a_(11),a_(12),a_(13)],[a_(21),a_(22),a_(23)],[a_(31),a_(32),a_(33)]| and A_(i j) is cofactors of a_(i j) , then value of Delta is given by

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

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

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