Let A,B,C,D be real matrices such that `A^(T)=BCD,B^(T)=CDA,C^(T)=DAB and D^(T)=ABC` for the matrix M=ABCD then find `M^(2016)`?

Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB and D^(T)=ABC for the matrix M=ABCD then find M^(3) ?

Let A, B, C, D be (not necessarily ) real matrices such that A^(T) = BCD , B^(T) =CDA, C^(T) = DAB and D^(T) =ABC for the matrix S = ABCD the least value of k such that S^(k) = S is

Let A, B, C, D be (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 , consider the two statements. I. S^3=S II. S^2=S^4 (A) II is true but not I (B) I is true but not II (C) both I and II are true (D) both I and II are false

If A is a nonsingular matrix such that A A^(T)=A^(T)A and B=A^(-1) A^(T) , then matrix B is

Let A and B be two square matrices of the same size such that AB^(T)+BA^(T)=O . If A is a skew-symmetric matrix then BA is

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

Consider three square matrices A, B and C of order 3 such that A^(T)=A-2B and B^(T)=B-4C , then the incorrect option is

Let A and B are square matrices of order 2 such that A+adj(B^(T))=[(3,2),(2,3)] and A^(T)-adj(B)=[(-2,-1),(-1, -1)] , then A^(2)+2A^(3)+3A^(4)+5A^(5) is equal to (where M^(T) and adj(M) represent the transpose matrix and adjoint matrix of matrix M respectively and I represents the identity matrix of order 2)

Let A and B be two matrices such that the order of A is 5xx7 . If A^(T)B and BA^(T) are both defined, then (where A^(T) is the transpose of matrix A)

If A is a non-singular matrix such that A A^T=A^T A and B=A^(-1)A^T , the matrix B is a. involuntary b. orthogonal c. idempotent d. none of these