Consider the (2 times 2) matrix (a) Show that (mathbf{S}) is orthogonal. (b) Perform a similarity transformation
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Consider the \(2 \times 2\) matrix
(a) Show that \(\mathbf{S}\) is orthogonal.
(b) Perform a similarity transformation with \(\mathbf{S}\) on each of the following matrices:
(c) Use the results from (b) to calculate the characters of the three transformed matrices.
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