How to create matrices and vectors in Sage
Type the rows of the matrix one by one.
A vector is just a matrix with one row or one column only. You can make it as a row vector and then transpose it if you like.
You multipley matrices just like numbers:
Random matrices and vectors
This box makes a random matrix of your desired size in a desired ring.
This box makes a random matrix of your desired size in a desired ring, but with small entries.
Sharable format
Cut-and-pastable output: you might want to cut and paste your matrix in and out of Sage. If you ask for the rows, you only need to adjust brackets a little. This is a good way to cut and paste them into discord.