1. Tardigrade
  2. Question
  3. Mathematics
  4. If B is a non-singular matrix and A is a square matrix, then det (B-1 AB) is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. If $B$ is a non-singular matrix and $A$ is a square matrix, then det $(B^{-1} AB)$ is equal to

VITEEEVITEEE 2010Determinants

Solution:

$det(B^{-1} AB)$
$= det(B^{-1})det\, A\, det\, B $
$= det(B^{-1}).det\, B.\, det\, A$
$= det(B^{-1} B).det \, A $
$= det \, I.\, det \, A$
$= 1\cdot det \, A= det \, A$