Why is this matrix multiplication not associative?

Questions
1

Apologies for the low quality of the attached image.

Presented is an attempt to calculate the product of six matrices of size 3x3.
The product: {{1,0,0},{0,1,0},{0,0,9}}

I then split the multiplication into two halves:
The product of the first half: {{1,0,0},{-1,1,0},{2,-4,1}}
The product of the second half: {{1,4,0},{0,1,3},{0,0,9}}

Multiplying these two matrices yields {{1,4,0},{-1,-3,3},{2,4,-3}}, which is correct. This is in fact the matrix which I row reduced to obtain the six elementary matrices in the original product.

Is there a reason why Wolfram|Alpha is computing the first result?

Six matrices

First three

Second three

First three, second three combined

issue.png
issue.png700×1800 92.5 KB

2

Taking a wild guess, the first one might be doing element-wise products rather than matrix multiplication.

3

That does make sense, thank you!

How might I “force” Wolfram to multiply normally? Moreover, why are the two smaller computations done normally?

4

Putting either a . or the word dot between each pair of matricies appears to make WolframAlpha perform matrix multiplication as you expect.

6 matricies with .

6 matricies with dot