Let A,B,C,D be real matrices such that A...

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)`?

`M^(2)`

`M^(3)`

`M^(4)`

Text Solution

Verified by Experts

The correct Answer is:

B, D

Topper's Solved these Questions

MATRICES & DETERMINANT
RESONANCE|Exercise EXERCISE-2|20 Videos
MATRICES & DETERMINANT
RESONANCE|Exercise PART-IV|6 Videos
MATRICES & DETERMINANT
RESONANCE|Exercise PART-II|27 Videos
INDEFINITE INTEGRATION
RESONANCE|Exercise SELF PRACTIC PROBLEMS|25 Videos
NUMBER THEORY
RESONANCE|Exercise Exercise -2 (PART - II)|4 Videos

Similar Questions

Explore conceptually related problems

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

If A and B are two matrices such that AB is defined; then (AB)^(T)=B^(T).A^(T)

For the following matrices,(A+B)^(T)=B^(T)+A^(T)=A^(T)+B^(T)

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

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

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

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)

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

RESONANCE-MATRICES & DETERMINANT-PART-III

Text Solution
|
Which one of the following is wrong?
Text Solution
|
Which of the following is true for matrox A=[{:(,1,-1),(,2,3):}]
Text Solution
|
Suppose a(1),a(2),a(3) are in A.P. and b(1),b(2),b(3) are in H.P. and ...
Text Solution
|
Let theta=(pi)/(5),X=[{:(,cos theta,-sin theta),(,sin theta,cos theta)...
Text Solution
|
If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|,then
Text Solution
|
Let a.b ,gt 0 and Delta=|{:(,-x,a,b),(,b,-x,a),(,a,b,-x):}|, then
Text Solution
|
The determination Delta=|{:(,b,c,balpha+c),(,c,d,calpha+d),(,balpha+c,...
Text Solution
|
The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,a...
Text Solution
|
If a non-singular matrix and A^(T) denotes the tranpose of A, then
Text Solution
|
Let "Let"(x)=|{:(,2sinx,sin^(2)x,0),(,1,2sin x,sin^(2)x),(,0,1,2sin x)...
Text Solution
|
Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}|,then
Text Solution
|
Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| whe...
Text Solution
|
If D is determinant of order three of Delta is a determinant formed by...
Text Solution
|
Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...
Text Solution
|
Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such t...
Text Solution
|
If A^(-1)=[{:(,1,-1,0),(,0,-2,1),(,0,0,-1):}] then
Text Solution
|
IF A and B are squre matrices of order 3, then the true statement is/a...
Text Solution
|
Let M be a 3xx3 non-singular matrix with det(M)=4,"If" M^(-1)"adj(adjM...
Text Solution
|
Let AX=B where A is 3 xx 3 and X and B are 3 xx 1 matrices then which ...
Text Solution
|