Let 
and a = 4, b = –2.
Show that:
A(BC) = (AB)C
To prove: A(BC) = (AB)C
LHS = A(BC) = 
⇒ LHS = 
⇒ LHS = 
⇒ LHS = 
RHS = (AB)C = 
Performing matrix multiplication as done for LHS
⇒ RHS = 
⇒ RHS = 
Clearly LHS = RHS = 
∴ A(BC) = (AB)C …proved
32
Let and a = 4, b = –2.
Show that:
A(BC) = (AB)C
To prove: A(BC) = (AB)C
LHS = A(BC) =
⇒ LHS =
⇒ LHS =
⇒ LHS =
RHS = (AB)C =
Performing matrix multiplication as done for LHS
⇒ RHS =
⇒ RHS =
Clearly LHS = RHS =
∴ A(BC) = (AB)C …proved