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.

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

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

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

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.

If matrix A = [a_(i j)]_(2 xx 2) , where a_(i j) = {("1 if",i ne j),("0 if",i = j):} then A^(2) is equal to

Let A=[a_(ij)]_(mxxn) be a matrix such that a_(ij)=1 for all I,j. Then ,

If matrix A=([a_(i j)])_(2xx2) , where a_(i j)={1,\ if\ i!=j0,\ if\ i=j , then A^2 is equal to I (b) A (c) O (d) I

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

If matrix A=[a_(ij)]_(2x2), where a_(ij)={{:(1"," , i ne j),(0",", i=j):} then A^(3) is equal to