Prove the following where A and B are square matrices of the same size

tr(A+B) = tr(A) + tr(B)

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the trace is the sum of the diagonal elements of a matrix

for A this would be: a11 + a22 + a33 + ... + ann

for B this would be: b11 + b22 + b33 + ... + bnn

adding these term by term we get: (a11+b11) + (a22+b22) + (a33+b33) + ... + (ann+bnn)

but this is just the trace of A+B

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