Question: Prove the following for matrices (A, B), and (C). a. ((A B) C=A(B C)). b. ((A B)^{T}=B^{T} A^{T}) c. (operatorname{tr}(A)) is invariant under similarity transformations.

Prove the following for matrices \(A, B\), and \(C\).

a. \((A B) C=A(B C)\).

b. \((A B)^{T}=B^{T} A^{T}\)

c. \(\operatorname{tr}(A)\) is invariant under similarity transformations.

d. If \(A\) and \(B\) are orthogonal, then \(A B\) is orthogonal.

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