Case Study-IIGautam 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 $AX = B$.(II) Find $\left|A\right|$.(III) Find $A^{-1}$.OR(III) Determine $P = A^2 - 5A$.