The trace of an n by n matrix A is the sum of the entries on its main diagnol and is denoted tr(A). Thus: $$tr(A) = a_{11}+a_{22} + ... + a_{nn}$$ . Let A and B be matrices by n matrices, prove the following:
(a). tr(A+B) = tr(A) + tr(B)
(b). tr(kA) = ktr(A)

Question

The trace of an n by n matrix A is the sum of the entries on its main diagnol and is denoted tr(A). Thus: $$tr(A) = a_{11}+a_{22} + ... + a_{nn}$$ . Let A and B be matrices by n matrices, prove the following:
(a). tr(A+B) = tr(A) + tr(B)
(b). tr(kA) = ktr(A)

beginnersmind · Answer

Add up two general matrices and apply the definition of the trace. Check if the equality holds.
Same for part b.