Question 1161807
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Having this assignment, the student SHOULD NOT think.


He (or she) simply MUST KNOW how to multiply matrices - - - and calculate A^2, directly and explicitly, on his (or her) own.


At this step, there is NOTHING to ask the tutors for help - - - it is THE STUDENTS' job.


When you establish this equality  A^2 = A + kI,  you will find the value of "k".


What follows, is simple.


This equality  A^2 = A + kI, can be written in the form

    A^2 - A = kI;


then factored

    A*(A-I) = kI


then presented in the form

    {{{A}}}.{{{((1/k)*(A-I))}}} = I,


and it means that the inverse matrix is equal

    {{{A^(-1)}}} = {{{(1/k)*(A-I)}}}.


So, your steps are


(a)  to establish / (to check) that  A^2 = A + kI  and find the value of "k".

     This step you MUST make on your own, as I just explained you.


(b)  Then the inverse matrix to A is  {{{A^(-1)}}} = {{{(1/k)*(A-I)}}}.
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Now, when I explained you every your step, I am waiting for your "THANKS" for my instructions.