Match the LIST-I with LIST-II
| LIST-I | LIST-II | ||
| (Matrix) | (Type of matrix) | ||
| A. | \( A=\left[a_{ij}\right]_{m\times m} \) where \( a_{ij}=0\ \forall\ i\ne j \) | I. | Scalar matrix |
| B. | \( A=\left[a_{ij}\right]_{m\times 1} \) | II. | Diagonal matrix |
| C. | \( A=\left[a_{ij}\right]_{1\times n} \) | III. | Column matrix |
| D. | \( A=\left[a_{ij}\right]_{m\times m} \) where \( a_{ij}=0\ \forall\ i\ne j \) and \( a_{ij}=k\ \forall\ i=j,k\ne 0 \) | IV. | Row matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-II, B-III, C-IV, D-I
A. \( A=\left[a_{ij}\right]_{m\times m} \) where \( a_{ij}=0\ \forall\ i\ne j \)
This matches II. Diagonal matrix.
A square matrix whose non-diagonal entries are all zero is a diagonal matrix; its diagonal entries may be different.
B. \( A=\left[a_{ij}\right]_{m\times 1} \)
This matches III. Column matrix.
It has m rows and only one column.
C. \( A=\left[a_{ij}\right]_{1\times n} \)
This matches IV. Row matrix.
It has only one row and n columns.
D. \( A=\left[a_{ij}\right]_{m\times m} \) where \( a_{ij}=0\ \forall\ i\ne j \) and \( a_{ij}=k\ \forall\ i=j,k\ne 0 \)
This matches I. Scalar matrix.
A diagonal matrix with all diagonal entries equal is a scalar matrix.
So the matching is A-II, B-III, C-IV, D-I.
Note: Some List-I items fit more than one List-II entry. Every scalar matrix is also a diagonal matrix, so (D) fits both (I) and (II). The question can still be solved because (A), a diagonal matrix whose diagonal entries need not be equal, fits only (II), (B) fits only (III) and (C) fits only (IV); Option (1) is the only option containing A-II.
NCERT (2026-27 edition):
Matrices
