Another matrix operation is the transpose - this operation reflects the entries of a matrix across its main diagonal. This amounts to switching the row and column for each entry.

This can be useful for detecting symmetry in data. If we have some data in a matrix, and we take the transpose and compare it to the original matrix, this tells us about how close our original data was to being symmetric.

Let \[A=\left[\begin{array}{cc} 1&-2\\ 1&3\end{array}\right].\] What is the transpose of \(A\)?

Let \[A=\left[\begin{array}{cc} 1&-2\\ 1&3\end{array}\right].\] What is the trace of \(A\)?

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