Science:Math Exam Resources/Courses/MATH152/April 2022/Question A13
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Question A13 

Find , where is a matrix that satisfies the equation and 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Solve for in the given equation. Is there a way to simplify the determinant? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. We start by rearranging the equation for , knowing that the matrix is invertible (it has nonzero determinant). This gives . Now, Now, compute We can compute and , and put this together with the above expression for to get . 