3.1 Multiplication of Matrices - Questions

This is a good place to use your calculator if it handles matrices. Do enough examples of each to convince yourself of your answer to each question. If your calculator does not handle matrices, or if you want a more mathematical argument, use generic matrices and carry out these operations like we did in the addition section.

Answer these questions on your own before you read beyond this paragraph. Remember to consider the dimensions of the matrices.

1. Consider . Does AB = BA for all B for which matrix multiplication is defined?

2. In general, does AB = BA?

3. Does A(BC) = (AB)C?

4. Does A(B + C) = AB + AC?

5. Does (AB)^T = B^TA^T?

6. Does A - B = -(B - A)?

7. For real numbers, if ab = 0, we know that either a or b must be zero. Is it true that AB = 0 implies that A or B is a zero matrix?

8. Are A^TA and AA^T always symmetric?