Rules of Matrix Arithmetic

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Theorems:

a)  A + B = B + A                    (Commutative law for addition)

b)  A + (B + C) = (A + B) + C       (Associative law for addition)

c)  A(BC) = (AB)C                  (Associative law for multiplication)

d)  A(B + C) = AB + AC            (Distributive law)

e)  (B + C)A = BA + CA            (Distributive law)

f)  A(B - C) = AB - AC

g)  (B - C)A = BA - CA

h)  a(B + C) = aB + aC

i)  a(B - C) = aB - aC

j)  (a + b)C = aC + bC

k)  (a - b)C = aC - bC

l)  (ab)C = a(bC)

m)  a(BC) = (aB)C = B(aC)

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A.5d