Which of the following statements are true?

I. Every identity matrix is a scalar matrix.

II. Every scalar matrix is a diagonal matrix.

III. Every diagonal matrix is a scalar matrix.

IV. Every zero matrix is a square matrix.

Explanation

1. 01

   An identity matrix is a scalar matrix whose diagonal elements are 1, and a scalar matrix is a diagonal matrix with equal diagonal elements: I and II are true.

2. 02

   $\begin{bmatrix} 1 & 0 \\ 0 & 2 \end{bmatrix}$ is diagonal but not scalar, so III is false; $\begin{bmatrix} 0 & 0 & 0 \end{bmatrix}$ is a zero matrix that is not square, so IV is false.