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Analyzing the matrix arithmetic operations
Learn about properties of matrix addition and multiplication, like commutativity, the associative property, and the distributive property.
Sal discusses the conditions of matrix dimensions for which addition or multiplication are defined.
Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way).
Sal shows that matrix multiplication is associative. Mathematically, this means that for any three matrices A, B, and C, (A*B)*C=A*(B*C).
Sal determines which of a few optional matrix expressions is equivalent to the matrix expression A*B*C. This is done using what we know about the properties of matrix addition and multiplication.