If `A=[a_(ij)]` is a square matrix of order 3 and `A_(ij)` denote cofactor of the element `a_(ij)` in `|A|` then the value of `|A|` is given by

A=[a_(ij)]_(mxxn) is a square matrix, if

If A = [a_(ij)] is a skew-symmetric matrix of order n, then a_(ij)=

If A=[a_(ij)] is a scalar matrix, then trace of A is

If A=[a_(ij)] is a scalar matrix of order nxxn and k is a scalar, then abs(kA)=

Let A=[a_(ij)]_(nxxn) be a square matrix and let c_(ij) be cofactor of a_(ij) in A. If C=[c_(ij)] , then

If A= (a_(ij)) is a 4xx4 matrix and C_(ij) , is the co-factor of the element a_(ij) , in Det (A) , then the expression a_11C_11+a_12C_12+a_13C_13+a_14C_14 equals-

Let A=[(1,1,1),(1,-1,0),(0,1,-1)], A_(1) be a matrix formed by the cofactors of the elements of the matrix A and A_(2) be a matrix formed by the cofactors of the elements of matrix A_(1) . Similarly, If A_(10) be a matrrix formed by the cofactors of the elements of matrix A_(9) , then the value of |A_(10)| is

Let A=[a_(ij)] be a square matrix of order 3 and B=[b_(ij)] be a matrix such that b_(ij)=2^(i-j)a_(ij) for 1lei,jle3, AA i,j in N . If the determinant of A is same as its order, then the value of |(B^(T))^(-1)| is

Let A=[a_(ij)] be a square matrix of order n such that {:a_(ij)={(0," if i ne j),(i,if i=j):} Statement -2 : The inverse of A is the matrix B=[b_(ij)] such that {:b_(ij)={(0," if i ne j),(1/i,if i=j):} Statement -2 : The inverse of a diagonal matrix is a scalar matrix.

Consider an arbitarary 3xx3 non-singular matrix A[a_("ij")] . A maxtrix B=[b_("ij")] is formed such that b_("ij") is the sum of all the elements except a_("ij") in the ith row of A. Answer the following questions : If there exists a matrix X with constant elemts such that AX=B , then X is