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### How do I define a list of products of matrices from a given list?

I'm trying to define a list of products of matrices from another list. This how I've tried to do it (using simplified data).

a = matrix(ZZ,[[1,0],[0,1]])
b = matrix(ZZ,[[0,1],[1,0]])
c = matrix(ZZ,[[1,1],[0,1]])
M=[a,b,c]
S=[X*Y for X, Y in M]
S


The output I get is

[0, 0, 1]


Obviously this is not the list of desired products, moreover it is not a list of matrices, and the list has 3 items rather than the 6 possible things that should occur. Beyond this simple example, I'd also like to be able to do this with longer products and more complicated initial lists.

### How do I define a list of products of matrices from a given list?

I'm trying to define a list of products of matrices from another list. This how I've tried to do it (using simplified data).

a = matrix(ZZ,[[1,0],[0,1]])
b = matrix(ZZ,[[0,1],[1,0]])
c = matrix(ZZ,[[1,1],[0,1]])
M=[a,b,c]
S=[X*Y for X, Y in M]
S


The output I get is

[0, 0, 1]


Obviously this is not the list of desired products, moreover it is not a list of matrices, and the list has 3 items rather than the 6 possible things that should occur. Beyond this simple example, I'd also like to be able to do this with longer products and more complicated initial lists.

This probably has a simple answer (I am a beginner). My next question though would be, how could I define a function that inputs some $l\in\mathbb{N}$ and outputs the list of products of that length?

### How do I define a list of products of matrices from a given list?

I'm trying to define a list of products of matrices matrices, of a set length, from another list. list of matrices. This how I've tried to do it (using simplified data).data and length 2).

a = matrix(ZZ,[[1,0],[0,1]])
b = matrix(ZZ,[[0,1],[1,0]])
c = matrix(ZZ,[[1,1],[0,1]])
M=[a,b,c]
S=[X*Y for X, Y in M]
S


The output I get is

[0, 0, 1]


Obviously this is not the list of desired products, moreover it is not a list of matrices, and the list has 3 items rather than the 6 possible things that should occur. Beyond this simple example, I'd also like to be able to do this with longer products and more complicated initial lists.

This probably has a simple answer (I am a beginner). My next question though would be, how could I define a function that inputs some $l\in\mathbb{N}$ and outputs the list of products of that length?