If A^(T).A^(-1) is symmetric, then A^(2)...

If `A^(T).A^(-1)` is symmetric, then `A^(2)`=

`A^(-1)`

`(A^(T))^(2)`

`A^(T)`

`(A^(-1))^(2)`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

APPLICATIONS OF MATRICES AND DETERMINANTS
PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (I. Choose the correct answer)|35 Videos
APPLICATIONS OF MATRICES AND DETERMINANTS
PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (II. Answer the following)|15 Videos
APPLICATIONS OF MATRICES AND DETERMINANTS
PREMIERS PUBLISHERS|Exercise SOLUTION TO EXERCISE 1.7|4 Videos
APPLICATIONS OF INTEGRATION
PREMIERS PUBLISHERS|Exercise Answer the following questions.|18 Videos
APPLICATIONS OF VECTOR ALGEBRA
PREMIERS PUBLISHERS|Exercise PROBLEMS FOR PRACTICE (Answer the following questions)|21 Videos

Similar Questions

Explore conceptually related problems

If A is symmetric then

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

A=[(3,a,-1),(2,5,c),(b,8,2)] is symmetric and B=[(d,3,a),(b-a,e,-2b-c),(-2,6,-f)] is skew-symmetric, then find AB.

If a and B are non-singular symmetric matrices such that AB=BA , then prove that A^(-1) B^(-1) is symmetric matrix.

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

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix, (ii) A -A^T is a skew-symmetric matrix and (iii) AA^T and A^TA are symmetric matrices.

If A is symmetric, prove that adj A is also symmetric.

If f(x) is a real-valued function defined as f(x)=In (1-sinx), then the graph of f(x) is (A) symmetric about the line x =pi (B) symmetric about the y-axis (C) symmetric and the line x=(pi)/(2) (D) symmetric about the origin

If A is symmetric as well as skew-symmetric matrix, then A is

If A, B are square materices of same order and B is a skewsymmetric matrix, show that A^(T)BA is skew-symmetric.

PREMIERS PUBLISHERS-APPLICATIONS OF MATRICES AND DETERMINANTS -SOLUTION TO EXERCISE 1.8

If A = [(2,0),(1,5)]" and B"=[(1,4),(2,0)] then |adj(AB)|=
Text Solution
|
If P = |(1,x,0),(1,3,0),(2,4,-2)| is the adjoint of 3xx3 matrix A and ...
Text Solution
|
If A = [{:(3," "1,-1),(2,-2," "0),(1," "2,-1):}] "and"" "A^(-1)=[(a(11...
Text Solution
|
If A, B and C are invertible matrices of some order, then which one of...
Text Solution
|
If (AB)^(-1)=[(12,-17),(-19,27)] "and"A^(-1)=[(1,-1),(-2,3)] "then"" "...
Text Solution
|
If A^(T).A^(-1) is symmetric, then A^(2)=
Text Solution
|
If A is a non-singular matrix such that A^(-1)=[(5,3),(-2,-1)], "then"...
Text Solution
|
A = [((3)/(5),(4)/(5)),(x,(3)/(5))] "and" A^(T)=A^(-1), then the value...
Text Solution
|
If A = [(1,tan""(theta)/(2)),(-tan""(theta)/(2),1)] and AB = I(2), the...
Text Solution
|
If A=[[cos theta,sin theta],[-sin theta,cos theta]] and A(adj A)=[[k,0...
Text Solution
|
If A=[(2,3),(5,-2)] be such that lambdaA^(-1) = A, then lambda is
Text Solution
|
If adj A=[[2,3],[4,1]] and adj B=[[1,-2],[-3,1]] then adj (AB) is :
Text Solution
|
The rank of the matrix [(1,2,3,4),(2,4,6,8),(-1,-2,-3,-4)] is
Text Solution
|
If x^(a)y^(b)=e^(m),x^(c)y^(d)=e^(n),Delta(1)=[(m,b),(n,d)]Delta(2)=[(...
Text Solution
|
Which of the following is/are correct ? (i) Adjoint of a symmetric m...
Text Solution
|
If rho (A) = rho ([A|B]), then the system AX = B of linear equations i...
Text Solution
|
If 0lt= thetalt=pi and the system of equations x+(sintheta)y- (costhet...
Text Solution
|
The augmented matrix of a system of linear equations is [(1,2,7,3),(0,...
Text Solution
|
Let A =[(2,-1,1),(-1,2,-1),(1,-1,2)] "and" 4B=[(3,1,-1),(1,3,x),(-1,1,...
Text Solution
|
If A = [(3,-3,4),(2,-3,4),(0,-1,1)], then adj (adj A) is
Text Solution
|