Prove that if A and B are matrices of the same size then trA

Prove that if A and B are matrices of the same size, then tr(A+B)=tr(A)+tr(B)

Given:

Goal:

Proof:

Solution

addition of matrix is additive

addition of matrix happens only when both sizes are same

trace is defined as sum of all the elements of diagonal of a matrix

while adding two matrices all the elements are added to their individual elements of same position

hence diagonal elements are added only to the diagonal elements

there fore

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