How do I write a Rust unit test that ensures that a panic has occurred?

You can find the answer in testing section of the Rust book. More specifically, you want #[should_panic] attribute:

#[test]
#[should_panic]
fn test_invalid_matrices_multiplication() {
    let m1 = Matrix::new(3, 4);  // assume these are dimensions
    let m2 = Matrix::new(5, 6);
    m1 * m2
}