(a) Let A be an invertible n x n and suppose that A-1 = A. Prove that det(A) = -1 or det(A) = 1. (b) Let A be a square matrix

Question

(a) Let A be an invertible n x n and suppose that A-1 = A. Prove that det(A) = -1 or det(A) = 1.
(b) Let A be a square matrix such that A² -7A+8I = 0 [where I and 0 are the identity matrix and the zero matrix, respectively). Show that det(A) # 0.

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