Show that A'A and AA ' are both symmetri...

Show that A'A and AA ' are both symmetric matrices for any matrix A.

Text Solution

Verified by Experts

The correct Answer is:

Hence ,A A is also symmetric matrix for any matrix A.

Doubtnut Promotions Banner Desktop Dark

Doubtnut Promotions Banner Mobile Dark

|

Topper's Solved these Questions

MATRICES
ARIHANT PUBLICATION|Exercise QUESTIONS FPR PRACTICE Part III (Transpose of a Matrix ,Symmetric and Skew -symmetric Matrices (Short Answer Type Questions)|8 Videos
MATRICES
ARIHANT PUBLICATION|Exercise QUESTIONS FPR PRACTICE Part IV (Inverse of a Matrix by Elementary Operations (Very Short Answer Type Questions ) |16 Videos
MATRICES
ARIHANT PUBLICATION|Exercise QUESTIONS FPR PRACTICE Part II (Multiplication of Matrices (Matrix Multiplecation) Short Answer Type Questions |16 Videos
LINEAR PROGRAMMING
ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (Long Answer Type Questions 6 Marks)|18 Videos
PROBABILITY
ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE(LONG ANSWER TYPE QUESTIONS)|17 Videos

Similar Questions

Explore conceptually related problems

Give an example of symmetric matrix.

If Aand B are both symmetric matrices of same oder,then prove that AB is symmetric if and only if AB=BA.

If A, B are symmetric matrices of same order, then find AB-BA .

What is AB – BA if A, B and AB are all symmetric matrices .

Let A and B are symmetric matrices of the same order. Prove that AB is symmetric if and if AB = BA.

If A and B are symmetric matrices , then prove that BA - 2AB is neither a symmetric matrix nor skew - symmetric matrix .

State True or False If A and B are symmetric matrices of the same order and AB-BA ne 0 , then AB is not symmetric .

State'True'or'false':If A and B are symmetric matrices of the same order and AB-BA !=0 , then AB is not symmetric

If A and B are symmetric matrices , then prove that AB+ BA is a symmetric matrix .

A matrix which is not symmetric is skew symmetric .

ARIHANT PUBLICATION-MATRICES -QUESTIONS FPR PRACTICE Part III (Transpose of a Matrix ,Symmetric and Skew -symmetric Matrices (Very Short Answer Type Questions)

Find the transpose of matrix [{:(-1,5,6),(sqrt(3),5,6),(2,3,-1):}].
01:06
|
If A=[{:(2,0),(1,4):}]andB=[{:(-1,2),(3,0):}] , then find (AB).
02:23
|
If A=[{:(-2,3),(1,2):}]andB=[{:(-1,0),(1,2):}], then find (A+2B).
02:04
|
If A=[{:(cosalpha,sinalpha),(-sinalpha,cosalpha):}] , then find the va...
04:52
|
Show that matrix A=[{:(1,-1,5),(-1,2,1),(5,1,3):}] is a symmetric mat...
02:13
|
Show that matrix A=[{:(0,1,-1),(-1,0,1),(1,-1,0):}]is a skew -symmetr...
02:23
|
Write a 3xx3 skew -symmetric matrix .
03:31
|
Write a 2xx2 matrix which is both symmetrc and skew -symmetric .
02:23
|
Show that A'A and AA ' are both symmetric matrices for any matrix A.
07:03
|
If A is symmetric , then show that B' AB is symmetric matrix .
02:41
|
If A and B are symmetric matrices , then prove that AB+ BA is a symme...
04:15
|
If A and B are symmetric matrices of the same order , then prove tha...
06:20
|
If matrix [{:(0,a,3),(2,b,-1),(c,1,0):}] is a skew -symmetric matrix...
03:42
|
If A is a skew -symmetric matrix , then show that A^(2) is a symmetri...
02:35
|