If `A=[a_("ij")]_(4xx4)`, such that `a_("ij")={(2",","when "i=j),(0",","when "i ne j):}`, then `{("det (adj (adj A))")/(7)}` is (where `{*}` represents fractional part function)

If A=(a_(ij))_(2xx2) .Where a_(ij) is given by (i-2j)^(2) then A is:

If A=[a_(ij)]_(mxxn) and a_(ij)=(i^(2)+j^(2)-ij)(j-i) , n odd, then which of the following is not the value of Tr(A)

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

If matrix A=[a_(ij)]_(3xx) , matrix B=[b_(ij)]_(3xx3) , where a_(ij)+a_(ji)=0 and b_(ij)-b_(ji)=0 AA i , j , then A^(4)*B^(3) is

Consider a matrix A=[a_("ij")] of order 3xx3 such that a_("ij")=(k)^(i+j) where k in I . Match List I with List II and select the correct answer using the codes given below the lists.

Statement 1: If A=([a_(i j)])_(nxxn) is such that ( a )_(i j)=a_(j i),AAi ,ja n dA^2=O , then matrix A null matrix. Statement 2: |A|=0.

If A= [{:(8,-4),(-5," "3):}] , verify that A(adj A)= (adj A) A= |A|I_(2) .

If a_(ij)=i^(2)-j and A=(a_(ij))_(2xx2) is:

If a_(ij)=(1)/(2) (3i-2j) and A = [a_(ij)]_(2xx2) is

Let A=([a_(i j)])_(3xx3) be a matrix such that AA^T=4Ia n da_(i j)+2c_(i j)=0,w h e r ec_(i j) is the cofactor of a_(i j)a n dI is the unit matrix of order 3. |a_(11)+4a_(12)a_(13)a_(21)a_(22)+4a_(23)a_(31)a_(32)a_(33)+4|+5lambda|a_(11)+1a_(12)a_(13)a_(21)a_(22)+1a_(23)a_(31)a_(32)a_(33)+1|=0 then the value of 10lambda is _______.