logo

Ask Questions, Get Answers

 
X
 Search
Want to ask us a question? Click here
Browse Questions
Ad
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Matrices
0 votes

A skew-symmetric matrix S satisfies the relation $S^2+I=0$ where $I$ is a unit matrix. Then $SS'$ is equal to

$(a)\;I\qquad(b)\;2I\qquad(c)\;-I\qquad(d)\;None\;of\;these$

Can you answer this question?
 
 

1 Answer

0 votes
Since $S$ is skew-symmetric matrix $S'=-S$
We have $S^2+I=0$
$S^2=-I+0$
$\quad\;=-I$
$S.S=-I$
$\Rightarrow S.S.S'=-IS'$
$\qquad\qquad=I(-S')$
$\qquad\qquad=IS$
$\qquad\qquad=S$
$S^{-1}SSS'=S^{-1}S$
(i.e) $ISS'=I$
$SS'=I$
$\Rightarrow $ If $SS'=I$ then $S$ is said to be an orthogonal matrix.
Hence (a) is the correct answer.
answered Nov 25, 2013 by sreemathi.v
 

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
...