Case Study-II
Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹ 160. From the same shop, Vikram buys 2 pens, 1 bag and 3 instrument boxes and pays a sum of ₹ 190. Also Ankur buys 1 pen, 2 bags and 4 instrument boxes and pays a sum of ₹ 250 .
Based on the above information, answer the following questions :
(I) Convert the given above situation into a matrix equation of the form $\mathrm{AX}=\mathrm{B}$.
(II) Find $\left|\mathrm{A}\right|$.
(III) Find ${\mathrm{A}}^{-1}$.
OR
(III) Determine $\mathrm{P}={\mathrm{A}}^2-5\mathrm{A}$.