Let A and B are two matrices of order $2\times 3$ and $3\times 2$ respectively with $det\left(AB\right)=7$

	Column-I		Column-II
P	det(BA) + det((AB)-1)	1	0
Q	det(I2 + AB) - det(I3 + BA)	2	$\frac{1}{7}$
R	$\det ({\mathrm{I}}_2-\mathrm{AB})-\det ({\mathrm{I}}_3-\mathrm{BA})-\frac{2}{7}$	3	$\frac{3}{7}$
S	$\det \left(\text{adj\hspace{0.17em}}\right(\text{adj\hspace{0.17em}}\left(\text{adj\hspace{0.17em}}\right(\text{adj\hspace{0.17em}\hspace{0.17em}}\mathrm{BA}\left)\right)\left)\right)+\frac{3}{7}$	4	$-\frac{2}{7}$
		5	$\frac{4}{7}$