Which of the following matrices are diagonal matrices?
A. \( \begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix} \)
B. \( \begin{bmatrix}1 & 2 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix} \)
C. \( \begin{bmatrix}1 & 0 & 0\\0 & 0 & 0\\0 & 0 & 1\end{bmatrix} \)
D. \( \begin{bmatrix}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix} \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, C and D only
A square matrix is a diagonal matrix if every entry off the main diagonal is 0. The diagonal entries themselves may be any numbers, including 0.
So only the off-diagonal entries decide: they are all 0 in A, C and D, while the (1, 2) entry of B is 2.
Checking the statements
(A) \( \begin{bmatrix}1 & 0 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix} \) — Correct. All entries off the diagonal are 0.
(B) \( \begin{bmatrix}1 & 2 & 0\\0 & 2 & 0\\0 & 0 & 3\end{bmatrix} \) — Incorrect. The (1, 2) entry is 2, which is off the diagonal.
(C) \( \begin{bmatrix}1 & 0 & 0\\0 & 0 & 0\\0 & 0 & 1\end{bmatrix} \) — Correct. All entries off the diagonal are 0; a zero on the diagonal is allowed.
(D) \( \begin{bmatrix}2 & 0 & 0\\0 & 2 & 0\\0 & 0 & 2\end{bmatrix} \) — Correct. All entries off the diagonal are 0 (it is also a scalar matrix).
NCERT (2026-27 edition):
Types of Matrices
