If the elements of a matrix A are real positive and distinct such that det `(A+A^T)^T=0` then

If A is a 3xx3 matrix such that det.A=0, then

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

Let A be any 3xx2 matrix. Then prove that det. (A A^(T))=0 .

If A is a non-singular matrix of order 3 and x is a real number such that det(xA)=abs(x)det(A) then the value of x is-

Let t be a real number satifying 2t ^(3) -9t ^(2) + 30 -lamda =0 where t =x + 1/xand lamda in R. If the above cubic has three real and distinct solutions for x then exhaustive set of value of lamda be :

If A^(T) is a skew-symmetric matrix and n is a positive integer, then A^(n) is