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The distributions will vary according to the base ring over which you are considering matrices.

To access, the documentation, open a Sage session and run

sage: random_matrix?

then hit the ENTER or RETURN key. This will display the documentation (in text mode).

Alternatively, run

sage: browse_sage_doc(random_matrix)

to display the documentation rendered in HTML.

You may also want to access the documentation for the random_element method of the base ring.

For example, type one of

sage: R = ZZ
sage: R = QQ
sage: R = GF(5)
sage: R = Zmod(12)

followed by one of

sage: R.random_element?
sage: browse_sage_doc(R.random_element)

The distributions will vary according to the base ring over which you are considering matrices.

To access, access the documentation, open a Sage session and run

sage: random_matrix?

then hit the ENTER or RETURN key. This will display the documentation (in text mode).

Alternatively, run

sage: browse_sage_doc(random_matrix)

to display the documentation rendered in HTML.

The corresponding page in the reference manual is accessible from this page:

http://doc.sagemath.org/html/en/reference/matrices/sage/matrix/special.html.

You may also want to access the documentation for the random_element method of the base ring.

For example, type one of

sage: R = ZZ
sage: R = QQ
sage: R = GF(5)
sage: R = Zmod(12)

followed by one of

sage: R.random_element?
sage: browse_sage_doc(R.random_element)