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# 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?

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