Can anybody help me out on this question? please explain nicely and clearly. Thank you for the help

2. Consider the following real matrix A (all calculations are ordinary real number calculations) 1 0 1 A=10 a 0 where a is, of course, a real number. (a) Compute A2, A3 and A4 Hint: refer to modules 19 and 20 if again necessary (b) Conjecture and prove by induction a formula for A", for all integers n 2 2 (c) Let S be the set of all matrices A as above, and let R be the set of all real numbers. Define a function by f(A) = a that entry of A in the middle. ls f one-to-one? Explain. (d) Is f onto? Explain. (e) Is fa bijection? Explain. 2. Consider the following real matrix A (all calculations are ordinary real number calculations) 1 0 1 A=10 a 0 where a is, of course, a real number. (a) Compute A2, A3 and A4 Hint: refer to modules 19 and 20 if again necessary (b) Conjecture and prove by induction a formula for A", for all integers n 2 2 (c) Let S be the set of all matrices A as above, and let R be the set of all real numbers. Define a function by f(A) = a that entry of A in the middle. ls f one-to-one? Explain. (d) Is f onto? Explain. (e) Is fa bijection? Explain