Match List-I with List-II.
| List-I | List-II | ||
| (A) | Diagonal Matrix | (I) | \(\begin{bmatrix}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{bmatrix}\) |
| (B) | Scalar Matrix | (II) | \(\begin{bmatrix}1 & 0 & 0\\ 0 & 2 & 0\\ 0 & 0 & 3\end{bmatrix}\) |
| (C) | Square Matrix | (III) | \(\begin{bmatrix}2 & 4\\ 3 & 5\end{bmatrix}\) |
| (D) | Identity Matrix | (IV) | \(\begin{bmatrix}5 & 0 & 0\\ 0 & 5 & 0\\ 0 & 0 & 5\end{bmatrix}\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
All four matrices are square, and (I), (II), (IV) are all diagonal, so each matrix gets its most specific name, one name per matrix. Start with the most special type.
(D) Identity Matrix
This matches (I): the only matrix with 1 in every diagonal place and 0 elsewhere.
(B) Scalar Matrix
This matches (IV): a diagonal matrix with all diagonal entries equal (here 5I), other than the identity.
(A) Diagonal Matrix
This matches (II): all off-diagonal entries are 0, but the diagonal entries 1, 2, 3 are different, so it is diagonal but not scalar.
(C) Square Matrix
This matches (III): a 2 × 2 matrix with non-zero entries off the diagonal, so it is square but of no special type.