logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  CBSE XII  >>  Math  >>  Matrices
+1 vote

If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is

 $$ \begin{array}{l   l}  (A) \quad \text{Skew symmetric matrix}  & (B) \quad \text{Symmetric Matrix}  \\ (C) \quad \text{Zero Matrix} & (D) \quad \text{Identity Matrix} \end{array} $$
Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • If A_{i,j} be a matrix m*n matrix , then the matrix obtained by interchanging the rows and column of A is called as transpose of A.
  • A square matrix A=[a$_{ij}$] is said to be skew symmetric if A'=-A that is $[a_{ij}]= -[a_{ji}]$ for all possible value of i and j.
  • A square matrix A=[a$_{ij}$] is said to be symmetric if A'=A that is $[a_{ij}]=[a_{ji}]$ for all possible value of i and j.
Given:
A and B are symmetric matrices
A=A'$\rightarrow$ transpose of A
B=B'$\rightarrow$ transpose of B
Now consider AB-BA
Taking transpose of it we get
(AB-BA)'=(AB)'-(BA)'
(AB)'-(BA)'= B'A'-A'B'
From the property of transpose of a matrix we have (AB)'=B'A'.
(AB-BA)'=B'A'-A'B'
Replacing A'=A and B'=B(Since A and B are symmetric matrix)
=BA-AB=-(AB-BA)( By taking out -1)
AB-BA is a skew symmetric matrix.
so (A) is the right option.
answered Mar 15, 2013 by sharmaaparna1
 

Related questions

Ask Question
student study plans
x
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App
...