Question

If P, Q, R & S are non singular matrix of order three such that PQRS = I then $R^{-1}$ is

• A. PQS
• B. QPS
• C. SPQ
• D. PSQ

Answer 1

The correct option is C SPQ

Given, PQRS = I

$\Rightarrow PQRS{S}^{-1}=I{S}^{-1}$
$\Rightarrow PQR=S^{-1}$
$\Rightarrow PQR{R}^{-1}=S^{-1}{R}^{-1}$
$\Rightarrow PQ=S^{-1}{R}^{-1}$
$\Rightarrow SPQ=S.S^{-1}{R}^{-1}=R^{-1}$
$\Rightarrow R^{-1}=SPQ$