# Compute determinant of matrix of Schur functions using Kronecker product

Given a matrix $m=(a_{i,j})$, where each $a_{i,j}$ is a Schur function,
by default, `m.det()`

will give the determinant using the original multiplication.

But I want it to use the Kronecker product for Schur functions.

I did not find any options to set the Kronecker product as default multiplication operator in the ring of Schur functions or in the matrix class.

To give an example, let us define such a matrix:

```
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: f = s[2]
sage: m = matrix([[f, 0], [0, f]])
sage: m
[s[2] 0]
[ 0 s[2]]
```

Then compare:

```
sage: m.det()
s[2, 2] + s[3, 1] + s[4]
sage: f * f
s[2, 2] + s[3, 1] + s[4]
sage: f.kronecker_product(f)
s[2]
```

Welcome to Ask Sage! Thank you for your question!

I edited your question to add a simple example of such a matrix, of size two by two.

This way others can copy and paste in a fresh Sage session to explore the question.

This increases the chances and the speed of an answer.

Does the example I added adequately illustrate the question? Otherwise please edit.

Yeah, you are right.