Question

If P,Q and R are $n\times n$ matrix and
det(P) = 2, det(Q) = 3 and det(R) = 5,
then find the value of $\det \left(P^2{\mathrm{QR}}^{-1}\right).$

• A. $\frac{5}{7}$
• B. $\frac{12}{5}$
• C. $\frac{7}{5}$
• D. $\frac{5}{12}$

Answer 1

The correct option is B $\frac{12}{5}$

$\mathrm{Given}\mathrm{that},\left(P\right|=2,\left(Q\right|=3,\left(R\right|=5.\mathrm{Now},\det \left(P^2{\mathrm{QR}}^{-1}\right)=\left(P^2{\mathrm{QR}}^{-1}\right|\mathrm{By}\mathrm{the}\mathrm{property}\mathrm{of}\mathrm{determinant},\det \left(P^2{\mathrm{QR}}^{-1}\right)=\frac{{\left(P\right|}^2\left(Q\right|}{\left(}=\frac{2^2\times 3}{5}=\frac{12}{5}\mathrm{option}\left(b\right)\mathrm{is}\mathrm{correct}$