When multiplying two matrices (A and B) to obtain the product AB = C, first pick any position in the product matrix.
In the sample below, you can pick the position by moving your mouse over that position.

Next, match the row of your chosen position with the row of A (the left factor), and match the column of your chosen position with the column of B (the right factor). If the lengths of the row and column differ, then the product does not exist. If the lengths of the row and column are the same, then multiply their corresponding numbers in pairs, left-to-right in the row, top-to-bottom in the column. The sum of these products is the entry in the chosen position of C. The result of combining the chosen row and column in this way is called their dot product.

In the example below, the entry (-14) in the bottom row is the sum (-2)(1) + (0)(-3) + (-3)(4).

Move the mouse arrow slowly across the product matrix on the right.
   Find this matrix product :  
-2 1
3 4
-1 2
3 1

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last updated 22 June 2007