This question doesn't look too hard but I just can't seem to figure it out.
Let $A$ and $B$ be n x n matrices. Show that if none of the eigenvalues of A are equal to 1, then the matrix equation $XA + B = X$ will have a unique solution.
2026-03-31 03:24:53.1774927493
Linear Algebra Eigenvalues question
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Hint: if none of the eigenvalues of $A$ is equal to 1, then $I-A$ is invertible.