exam Maths Puzzle Numerical Ability

If A is a square matrix with the property (A with an exponet of 2) = 0, show that (I - A)inverse = A + I.


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On page 224 number 5, I am not sure how to work it. Can you show me the step by step solution to be able to solve the others? Also, do you have any tips on how to solve these probl define similar