Question

Match List-I with List-II
List-I
a) A matrix which is not a square matrix
b) A square matrix $A' = A$
c) The diagonal elements of a diagonal matrix are same
d) A matrix which is both symmetric and skew symmetric
List-II
i) Symmetric matrix
ii) Null matrix
iii) Rectangular matrix
iv) Scalar matrix
Codes:

• A. a - iii, b - i, c - iv, d - ii
• B. a - iii, b - ii, c - iv, d - i
• C. a - i, b - ii, c - iv, d - iii
• D. a - iii, b - iv, c - i, d - ii

Hint:

The fact that the Null (zero) square matrix is the only matrix that is both symmetric and skew-symmetric is a classic true/false or matching question concept. It is derived directly from setting $A = -A$.

Answer 1

The Correct Option is A

To solve the problem of matching List-I with List-II, we need to understand the properties of different types of matrices.

1. List-I Correspondence:
   • a) A matrix which is not a square matrix.
   • b) A square matrix where \( A' = A \).
   • c) A diagonal matrix with the same diagonal elements.
   • d) A matrix which is both symmetric and skew symmetric.
2. List-II Identifications:
   • i) Symmetric matrix
   • ii) Null matrix
   • iii) Rectangular matrix
   • iv) Scalar matrix

Step-by-Step Analysis:

• Option a - iii: Rectangular Matrix
  A matrix that is not a square matrix is a rectangular matrix. Here, the number of rows is not equal to the number of columns.
• Option b - i: Symmetric Matrix
  A symmetric matrix is defined as a square matrix that satisfies \( A' = A \) (the transpose of the matrix is equal to the matrix itself).
• Option c - iv: Scalar Matrix
  A diagonal matrix where all diagonal elements are the same is known as a scalar matrix.
• Option d - ii: Null Matrix
  A matrix that is both symmetric and skew-symmetric (and still valid) is a null matrix, where all elements are zero.

Conclusion: The correct matching of the two lists is:
a - iii, b - i, c - iv, d - ii.