Ask Questions, Get Answers

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

If a square matrix A is such that $AA^T=I=A^TA$ then $|A|$ is equal to

$\begin{array}{1 1}(A)\;0&(B)\;\pm 1\\(C)\;\pm 2&(D)\;\text{None of these}\end{array}$

Can you answer this question?

1 Answer

0 votes
Given A is a square matrix and $AA^T=I=A^TA$
$\Rightarrow |AA^T|=|I|=|A^TA|$
$\Rightarrow |A||A^T|=1=|A^T||A|$
$\Rightarrow |A|^2=1$
$\Rightarrow |A|=\pm 1$
Hence (B) is the correct answer.
answered Apr 25, 2014 by sreemathi.v

Related questions

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