Wolfram Research
Wolfram Math World: Math World: Matrix Multiplication
Explains how to perform matrix multiplication, including how to perform products on two block matrices. Also has links to related topics.
CK-12 Foundation
Ck 12: Algebra: Limitations of Matrix Multiplication
[Free Registration/Login may be required to access all resource tools.] This lesson shows you how to determine if two matrices can be multiplied together and explains that the commutative property does not apply.