Answer
See proof below.
Work Step by Step
From the properties of matrices and that $c$ , $d$ are real values, we get:
$(c+d)A=(c+d)[a_{ij}]=[(c+d)a_{ij}]=[c* a_{ij}+d* a_{ij}]=[c* a_{ij}]+[d* a_{ij}]=c*[a_{ij}]+d*[a_{ij}]=cA+dA$
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