Linear Algebra Help - Proof Problem
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Linear Algebra Help - Proof Problem

[From: ] [author: ] [Date: 11-05-06] [Hit: ]
b) show that 2A^2 - 3A + I is symmetric.-Not all A^2 is invertible.......
I really hate these proofs, I'm great at the math, but it's the proofs that kill me. Here's my problem.

Let A be an n by n matrix.

a) show that A^2 is invertible
b) show that 2A^2 - 3A + I is symmetric.

-
Not all A^2 is invertible.

If determinant of A is zero then A^2 is not invertible

because det(A^2) = [ det(A) * det (A) ]
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