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 (s) good :

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,,", then which of the following"),(0,,"otherwise",):} hold (s) good :

Let A=[a_("ij")] be a matrix of order 2 where a_("ij") in {-1, 0, 1} and adj. A=-A . If det. (A)=-1 , then the number of such matrices is ______ .

Let A be the 2 xx 2 matrix given by A=[a_("ij")] where a_("ij") in {0, 1, 2, 3, 4} such theta a_(11)+a_(12)+a_(21)+a_(22)=4 then which of the following statement(s) is/are true ?

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)

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

If a square matix a of order three is defined A=[a_("ij")] where a_("ij")=s g n(i-j) , then prove that A is skew-symmetric matrix.

The matrix A given by (a_(ij))_(2 xx 2) if a_(ij) = i - j is ………. .

Let P=[a_("ij")] be a 3xx3 matrix and let Q=[b_("ij")] , where b_("ij")=2^(i+j) a_("ij") for 1 le i, j le 3 . If the determinant of P is 2, then the determinant of the matrix Q is

Detemine the matrix A = (a_(ij))_(3 xx 2) if a_(ij) = 3i - 2j

Construct a 3 xx 3 matrix whose elements are a_(ij) = i^(2)j^(2)