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Easy: Matrix times a column
Each entry of AB comes from a row of A and a column of B: multiply the matching entries and add. The entry in row i, column j uses row i of A and column j of B. The number of columns of A must equal the number of rows of B, and AB is usually not equal to BA.
Find the product.
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Each entry of the product is a row of the first matrix times a column of the second: multiply matching entries and add. The entry in row 1, column 2 uses row 1 and column 2.
Generally not. Matrix multiplication isn't commutative, so the order matters, and sometimes only one order is even defined.
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