Question: Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3. The trace of an n x n matrix

Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3.
The trace of an n x n matrix A = [aij], denoted Tr A, is the sum of the diagonal elements:

1. Tr(A+B) = TrA + TrB
2. Tr(cA) = cTrA
3. Tr (AT) =Tr A?

= aji + a22 + akk. + ann = k=1

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