Match the LIST-I with LIST-II
| LIST-I | LIST-II |
| Characteristic of square matrix | Type of matrix |
| A. A is a square matrix such that \( A+A^T=0 \). | I. Identity matrix or scalar matrix |
| B. B is a square matrix such that \( B^2=B \) | II. Diagonal matrix |
| C. C is a square matrix with all equal diagonal element and all the non-diagonal elements are zero. | III. Skew symmetric matrix |
| D. D is a matrix such that all the non-diagonal elements are zero. | IV. Idempotent matrix |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A-III, B-IV, C-I, D-II
(A) A is a square matrix such that \( A+A^T=0 \).
This matches III. Skew symmetric matrix. \( A^T=-A \) is the definition of a skew symmetric matrix.
(B) B is a square matrix such that \( B^2=B \)
This matches IV. Idempotent matrix. A matrix with \( B^2=B \) is called idempotent.
(C) C is a square matrix with all equal diagonal element and all the non-diagonal elements are zero.
This matches I. Identity matrix or scalar matrix. A diagonal matrix with equal diagonal entries is a scalar matrix (the identity matrix when the entries are 1).
(D) D is a matrix such that all the non-diagonal elements are zero.
This matches II. Diagonal matrix. All entries off the diagonal are zero, and the diagonal entries need not be equal.
So the matching is A-III, B-IV, C-I, D-II.