Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Type of matrix | Conditions | ||
| (A) | Square matrix A | (I) | \(A= [a_{ij}]_{m\times m}\) where \(\begin{cases}a_{ij}=0 & ,i\ne j\\a_{ij}=k & ,i=j\end{cases}\), where \(k\ne 0\) is constant. |
| (B) | Scalar Matrix A | (II) | \(A= [a_{ij}]_{m\times m}\) |
| (C) | Diagonal matrix A | (III) | \(A= [a_{ij}]_{m\times m}\) where \(\begin{cases}a_{ij}=0 & ,i\ne j\\a_{ij}=1 & ,i=j\end{cases}\) |
| (D) | Identity matrix A | (IV) | \(A= [a_{ij}]_{m\times m}\) where \(a_{ij} = 0, i\ne j\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
Each condition in List-II is matched with the type of matrix it defines.
(A) Square matrix A
This matches (II). A square matrix only needs as many rows as columns, \(A = [a_{ij}]_{m\times m}\), with no condition on the entries.
(B) Scalar Matrix A
This matches (I). A scalar matrix is a diagonal matrix whose diagonal entries are all equal to the same constant k.
(C) Diagonal matrix A
This matches (IV). A diagonal matrix only needs \(a_{ij} = 0\) for \(i \ne j\); its diagonal entries may be any numbers. Conditions (I) and (III) fix the diagonal entries, so they describe only some diagonal matrices.
(D) Identity matrix A
This matches (III): every off-diagonal entry is 0 and every diagonal entry is 1.
So the matching is (A)-(II), (B)-(I), (C)-(IV), (D)-(III).
Tip: When some items fit more than one entry, match the items with only one possible match first.
Note: Some List-I items fit more than one List-II entry. Every matrix in List-I is a square matrix, so each fits (II); a scalar matrix also fits (IV); an identity matrix also fits (IV), and (I) with k = 1. The question can still be solved because (A) Square matrix has only one possible match, (II), and (C) Diagonal matrix then has only one possible match, (IV); Option (4) is the only option containing (C)-(IV).
NCERT (2026-27 edition):
Matrices
