Distributive Property

The distributive property deals with a matrix expression that contains both matrix multiplication and matrix addition. Go through the following steps to demonstrate the property.

1. Add the right two matrices together, click = to check your result, below.	+
2. Multiply the first matrix times the result. Click "=" to check your result.
3. Now, work the problem again by forming the product of the left matrix and each of the others.	+
4. Finally, add up the two products.	+

Both results are the same, demonstrating that matrix multiplication is distributive over matrix addition:

A(B + C) = AB+AC

It is also true that

(X + Y)Z = XZ+YZ

For more practice, change the elements in the matrices of step 1 (only), and then work the problem again. When you make changes, replace the contents of a cell with an integer (only) and click outside of the cell to make the change.