In a square matrix A of order 3 the elements `a_(ij)` 's are the
sum of the roots of the equation `x^(2) - (a+b) x + ab =0,`
`a_(I,i+1)`'s are the product of the roots, `a_(I,i-1)` 's are all unity
and the rest of the elements are all zero. The value of the det (A) is equal to

construst a matrix of order 2 xx 2 whose elements are defined as a_(ij)=i+3j.

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

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

The square matrix A=[a_(ij)" given by "a_(ij)=(i-j)^3 , is a

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.

Elements of a matrix A of order 10 x 10 are defined as a_(ij)=omega^(i+j) (where omega is cube root unity), then tr(A) of matrix is

For a 2xx2 matrix A=[a_(i j)] whose elements are given by a_(i j)=i/j , write the value of a_(12) .

Construct a 3xx4 matrix A=[a_(i j)] whose elements a_(i j) are given by: ) a_(i j)=2i

If A=[a_(i j)] is a scalar matrix of order nxxn such that a_(i i)=k for all i , then trace of A is equal to n k (b) n+k (c) n/k (d) none of these

If A is a 3xx3 matrix, whose elements are given by a_(i j)=1/3|-3i+j|,\ then write the value of a_(23) .