Properties Of Matrix Multiplication

1. Not commutative. A\times B \neq B\times A
2. Associative. (A\times B)\times C = A\times (B\times C)

e.g. For A \times B where A is m\times n matrix and B is n\times m matrix,
A\times B is an m\times m matrix,
B\times A is an n\times n matrix.

Identity matrix
Denoted as I or I_{n\times n}
e.g.

    \[\begin{bmatrix}   1 & 0 & 0 \newline    0 & 1 & 0 \newline    0 & 0 & 1 \newline   \end{bmatrix}\]

For any matrix A, A\times I=I\times A=A

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