Let A,B,C,D are (not necessarily square) real matrices such that
`A^(T) = BCD , B^(T) = CDA, C^(T) = DAB and D^(T) = ABC` for the matrix `S = ABCD `prove that `S^(3) = S`.

Let A and B are two square matrices such that AB = A and BA = B , then A ^(2) equals to : a)B b)A c)I d)O

Suppose A and B are two symmetric matrices. Prove that (AB)^T = BA

Let A be a square matrix. Then prove that A + A ^(T) is a symmetric matrix.

Let A be a square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.

If A and B are square matrices of the order and if A=A^(T),B=B^(T) , then (ABA)^(T) is equal to a) BAB b) ABA c)ABAB d) AB^(T)

Let A be a square matrix. Then prove that A - A^(T) is a skew-symmetric matrix

For the reversible isothermal process Delta S is given by (1) ΔH / ΔT (2) T /q (3) q × T (4) q rev / T

If A is a square matrix of order 3, then value of |(A - A^(T))^(2005) | is equal to A)1 B)3 C)-1 D)0

Let A and B be 3 xx 3 matrices of real numbers, where A is symmetric , B is skew symmetric and (A + B) (A - B) = (A - B) ( A + B). If (AB)^(t) = (-1)^(k) AB , where (AB)^(t) is the transpose of the matrix AB, then k is a)any integer b)odd integer c)even integer d)cannot say anything