Practice question · Select all that apply
Let A be 3 x 2 and B be 2 x 3. Select every statement that is TRUE.
Hints
- Check the inner dimensions in each order separately, both may work but give different shapes.
- Addition needs identical shapes, and 3 x 2 is not 2 x 3.
Show the answer
- A. AB is defined and is 3 x 3
- B. BA is defined and is 2 x 2
- E. AB and BA have different shapes
Why
AB is 3 x 3 and BA is 2 x 2: both exist, but they are not even the same size, so they cannot be equal. Addition fails because the shapes differ. This is the strongest possible form of non-commutativity, the two orders live in different spaces entirely.
Practise Matrices and Matrix Operations
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