logo

Ask Questions, Get Answers

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

Let A and B be the square matrices of the order $3\times 3$.Is $(AB)^2=A^2B^2?$ Give reasons

Can you answer this question?
 
 

1 Answer

0 votes
Toolbox:
  • $(AB)^2=(AB)(AB)$
Step1:
To prove:
$(AB)^2=A^2B^2$
Consider LHS:-
$(AB)^2=(AB)(AB)$
$\;\;\;\;\;\;\;\;\;=A.A\; B.B$
$\;\;\;\;\;\;\;\;\;=A^2\; B^2$ [When AB=BA]
$\Rightarrow (AB)^2=A^2B^2$
$\Rightarrow (AB)^2=RHS$
Hence LHS=RHS
answered Mar 23, 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
...