Which of the following statements are correct? (A) Every diagonal mat…

The correct answer is Option (4) → (B) and (C) only

A diagonal matrix is a square matrix whose non-diagonal elements are all zero. A scalar matrix is a diagonal matrix whose diagonal elements are all equal. The identity matrix is a square matrix with every diagonal element 1 and every other element 0. A zero matrix is a matrix whose elements are all zero, and it can be of any order.

For example,

    \( \displaystyle \begin{bmatrix} 2 & 0 \\ 0 & 5 \end{bmatrix} \) is diagonal, but its diagonal elements are not equal

    \( \displaystyle \begin{bmatrix} 0 & 0 \end{bmatrix} \) is a zero matrix of order \(1 \times 2\)

So a diagonal matrix need not have equal diagonal elements, a scalar matrix is always diagonal, I has all its diagonal elements equal to 1, and a zero matrix can be of order m × n with m ≠ n.

Checking the statements

(A) Every diagonal matrix is a scalar matrix. — Incorrect. \(\begin{bmatrix} 2 & 0 \\ 0 & 5 \end{bmatrix}\) is diagonal but not scalar.

(B) Every scalar matrix is a diagonal matrix. — Correct. A scalar matrix is a diagonal matrix with equal diagonal elements.

(C) The identity matrix is a scalar matrix. — Correct. It is diagonal and every diagonal element is 1.

(D) Every zero matrix is a square matrix. — Incorrect. \(\begin{bmatrix} 0 & 0 \end{bmatrix}\) is a zero matrix of order \(1 \times 2\).