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 $$A X=B$$.

(ii) Find $$|\mathrm{A}|$$.

(iii) Find $$\mathrm{A}^{-1}$$.

OR

(iii) Determine $$P=A^2-5 A$$.