If `A subB`, then compute B'-A'.

If A and B are square matrices of the same order such that AB = BA, then compute (2A + B) (A + 2 B).

If A is of order 2 xx 3 . Is it possible to compute A^2 ?

If A and B are square matrices of the same order, compute (A+B). (A-B)

If A = [(3,1),(-1,2)] , then compute A^5 without computing A^3 and higher powers of A.

If A = [(1,1),(1,1)] , compute A^3

Compute (98)^5

In each of the following problems, clearly state what the relevant and irrelevant factors are while going through Steps 1, 2 and 3 given in this chapter :- Suppose a company needs a computer for some period of time. The company can either hire a computer for Rs 2,000 per month or buy one for Rs 25,000. If the company has to use the computer for a long period, the company will pay such a high rent, that buying a computer will be cheaper. On the other hand, if the company has to use the computer for say, just one month, then hiring a computer will be cheaper. Find the number of months beyond which it will be cheaper to buy a computer.

In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

Let '*' be the binary operation defined on Q by the rule a * b = ab^2 for a , b in Q. compute (1*2) *3.