Question: Q2.1 Given two matrices, A 2 Rmn and B 2 Rmn, prove that where ai j and bi j denote an element in the matrices

Q2.1 Given two matrices, A 2 Rmn and B 2 Rmn, prove that

m tr(ATB) = tr(ABT) = tr(BAT) = tr(BTA) = aij bij, i=1

where ai j and bi j denote an element in the matrices A and B, respectively.

m tr(ATB) = tr(ABT) = tr(BAT) = tr(BTA) = aij bij, i=1 j=1

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