Which of the following is (are) NOT the square of a 3x3 matrix with real entries?

The correct options are A ⎡⎢⎣10001000𕒵⎤⎥⎦ and D ⎡⎢⎣𕒵000𕒵000𕒵⎤⎥⎦.
For A and D, det(A²) = |10001000𕒵|² = 𕒵.
| 𕒵000𕒵000𕒵 |
Consider ⎡⎢⎣10001𕒶01𕒵⎤⎥⎦ ⎡⎢⎣10001𕒶01𕒵⎤⎥⎦ = ⎡⎢⎣1000𕒵000𕒵⎤⎥⎦
For C, I² = ⎡⎢⎣100010001⎤⎥⎦. Hence, A and D are NOT the square of a 3x3 matrix with real entries.