Question: Let A be an invertible, square matrix. a) Write det(A 2 ) in terms of det(A). b) Suppose that A is also idempotent, that is,

Let A be an invertible, square matrix.

a) Write det(A2) in terms of det(A).

b) Suppose that A is also idempotent, that is, A2 = A. Calculate det(A).

c) Give an example of a 3 3 invertible, idempotent matrix. (There's only one.)

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