- #1
Mr Davis 97
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Homework Statement
If ##A## is an ##n \times n## matrix, show that the eigenvalues of ##T(A) = A^{t}## are ##\lambda = \pm 1##
Homework Equations
The Attempt at a Solution
First I assume that a matrix ##M## is an eigenvector of ##T##. So ##T(M) = \lambda M## for some ##\lambda \in \mathbb{R}##. This means that ##M^t = \lambda M##. Then ##\det (M^t) = \det (M)##. So ##\det(M) = \lambda^n \det (M)##. But I can't seem to cancel the determinants since we don't know if ##M## is invertible or not. This is where I get stuck.