Answer
See proof below.
Work Step by Step
From the properties of matrices, we have that
$(cd) A=(cd) [a_{ij}]$ , and c,d are real numbers
Then, $(cd) A=(cd) [a_{ij}]= [(cd)a_{ij}] $
Since c,d and $a_{ij}$ are real numbers, then
$(cd) A=(cd) [a_{ij}]= [(cd)a_{ij}]= [c(da_{ij}])=c[da_{ij}]=c(dA)$