I have tried everything in my knowledge and couldn't get a grasp of what the answer should be. Only thing that remains is a booklet formula for A^-1 = adj(A).1/det(A) but that doesn't make sense as it doesn't use the first equation. Can you give me some insight?
2026-05-04 20:09:44.1777925384
Let $(I − A)^2 + A = 0,$ and suppose that the inverse of the square matrix $A$ exists. Write down a formula for $A^{−1}$ in terms of $A$
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$(I-A)^2+A=0$ $\implies I^2+A^2-2A+A=0$ $\implies A^2-A=-I \implies A^{-1}=I-A$