Let `A = {a _(ij)} be a 3 xx 3` matrix, where
`a_(ij) {{:( (-1) ^( j -i) if i lt j","),( 2 if i=j","),( (-1) ^(i+j) if i gt j","):}`
then det `(3 Adj (2 A ^(-1)))` is equal to _____________

If element of matrix A is defined as A=[a_(ij)]_(3xx3) where A={((-1)^(j-i),,iltj),(2,,i=j),((-1)^(j+i),,i gtj):} , then the value of abs(3Adj(2A^-1) is

Let A=|a_(ij)|" be a "3xx3 matrix where a_(ij)={{:((i^(j)-j^(i)+2ij)x,iltj),(1,igtj","),(0,i=j):} , then the minimum value of |A| is equal to (where x is a real number)

Construct a 3xx3 matrix whose elements are given by a_(ij)={{:((1)/(2)|2i-3j|","i!=j),(|2i-j|","i=j):}

Construct a matrix [a_(ij)]_(3xx3) , where a_(ij)=2i-3j .

Construct a 2xx2 matrix, where (i) a_("ij")=((i-2j)^(2))/(2) (ii) a_("ij")=|-2i+3j|

Let A = [a_(ij)] be 3 xx 3 matrix given by a_(ij) = {(((i+j)/(2))+(|i-j|)/(2),if i nej,),((i^(j)-(i.j))/(i^(2)+j^(2)),if i n=j,):} where a_(ij) denotes element of i^(th) row and j^(th) column of matrix A. On the basis of above information answer the following question: If a 3 xx3 matrix B is such that A^(2) +B^(2) = A +B^(2)A , then det. (sqrt(2)BA^(-1)) is equal to

Let A = [a_(ij)] be 3 xx 3 matrix given by a_(ij) = {(((i+j)/(2))+(|i-j|)/(2),if i nej,),((i^(j)-(i.j))/(i^(2)+j^(2)),if i =j,):} where a_(ij) denotes element of i^(th) row and j^(th) column of matrix A . On the basis of above information answer the following question: If A^(2)+ pA + qI_(3) = 32 A^(-1) , then (p +q) is equal to-

Let A=a_(ij) be a matrix of order 3, where a_(ij)={{:(x,,if i=j","x in R),(1,,if |i-j|=1),(0,,"otherwise"):} then which of the following hold good :