Question

Which 3 x 3 matrix represents a reflection in the yz plane followed by inversion through the origin?

Answer 1

That would be the product of the matrices of the two operations, done in that order. The first matrix changes x tp -x, and leaves y and z the same. The second matrix changes x to -x, y to -y and z to -z.

The product matrix leaves x unchanged and changes y to -y and z to -z.
The resulting matrix would seem to be
1...0...0
0.. -1..0
0...0..-1