Question

In the following bit of mathematica code

a1 = {{0, -I}, {I, 0}}
a2 = {{0, 1}, {1, 0}}
a3 = {{1, 0}, {0, -1}}
c = I*a1*a2 // MatrixForm
d = c*a3 // MatrixForm

The display of d shows up as a two by two matrix, where the 1,1 and 2,2 elements are themselves 2×2 matrixes, whereas I expect it to be a plain old 2×2 matrix of scalars?

Answer 1

use () to protect expression from MatrixFrom which is a wrapper.
use '.' for matrix multiplication. Not '*'

a1 = {{0, -I}, {I, 0}}
a2 = {{0, 1}, {1, 0}}
a3 = {{1, 0}, {0, -1}}
(c = I a1.a2) // MatrixForm
(d = c.a3) // MatrixForm

This is the output I get for d:

(1  0
 0  1)