Statement 1: The inverse of singular matrix `A=([a_(i j)])_(nxxn), \ w h e r e \ a_(i j)=0,igeqj \ i s \ B=([a i j^-1])_(nxxn)`.
Statement 2: The inverse of singular square matrix does not exist.

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

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

Show that : The determinant of a matrix A=([a_(i j)])_(5xx5) where a_(i j)+a_(j i)=0 for all i and j is zero.

Statement-1 (Assertion and Statement- 2 (Reason) Each of these questions also has four alternative choices, only one of which is the correct answer. You have to select the correct choice as given below. Statement-1 The determinant fo a matrix A= [a_(ij)] _(nxxn), where a_(ij) + a_(ji) = 0 for all i and j is zero. Statement- 2 The determinant of a skew-symmetric matrix of odd order is zero.

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.

Construct 3times4 matrix A=[a_(i j)] whose elements are given by a_(i j)=i+j

If matrix A=[a_(ij)]_(2X2) , where a_(ij)={[1,i!=j],[0,i=j]}, then A^2 is equal to

If matrix A=[a_(ij)]_(2X2) , where a_(ij)={[1,i!=j],[0,i=j]}, then A^2 is equal to

Construct a 2xx2 matrix A=[a_(i j)] whose elements are given by a_(i j)=(i+j)^2 .

Find the adjoint of matrix A=[a_(i j)]=[(p, q),( r, s)] .