In this exercise we show that matrix multiplication is distributive over matrix addition.a) Suppose that A and B arc m × k matrices and that C is a k × n matrix. Show that (A + B)C = AC + BC.________________b) Suppose that C is an m × k matrix and that A and B are k × n matrices. Show that C(A + B) = CA + CB.

SolutionStep 1:In this problem we have to show that matrix multiplication is distributive over matrix addition.Step 2: a) Suppose that A and B are m × k matrices and that C is a k × n matrix. Show that (A + B)C = AC + BC. Therefore (A+B) + Now (A+B)C (multiply C matrix with AXB) Which is Step 3: Take right hand side AC= Similarly BC= Adding both matric AC+BCWe get Therefore we can say (A + B)C = AC + BC Hence, it is proved that matrix multiplication is distributive over matrix addition.