- #1
Mr Davis 97
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Homework Statement
Suppose that a square matrix ##A## satisfies ##(A - I)^2 = 0##. Find an explicit formula for ##A^{-1}## in terms of ##A##
Homework Equations
The Attempt at a Solution
From manipulation we find that ##A^2 - 2A + I = 0## and then ##A(2I - A) = I##. This shows that if we right-multiply ##A## by ##2I - A##, we get the identity matrix. However, to show that ##2I - A## is an inverse, don't we also have to show that we can left-multiply ##A## by ##2I - A## such that ##(2I - A)A = I##? I don't see how we can do that...