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

Step 1: Identify definitions

• Rectangular matrix: number of rows $\neq$ number of columns
• Symmetric matrix: $A' = A$
• Scalar matrix: diagonal matrix with equal diagonal elements
• Null matrix: all elements are zero

Step 2: Match each item
(a) A matrix which is not a square matrix
\[ \Rightarrow \text{Rectangular matrix} (iii) \] (b) A square matrix $A' = A$
\[ \Rightarrow \text{Symmetric matrix} (i) \] (c) Diagonal elements of a diagonal matrix are same
\[ \Rightarrow \text{Scalar matrix} (iv) \] (d) A matrix both symmetric and skew symmetric
\[ A' = A \text{and} A' = -A \] \[ \Rightarrow A = -A \Rightarrow 2A = 0 \Rightarrow A = 0 \] \[ \Rightarrow \text{Null matrix} (ii) \]
Step 3: Final matching
\[ a \rightarrow iii, b \rightarrow i, c \rightarrow iv, d \rightarrow ii \] Final Answer:
\[ \boxed{\text{Option (1)}} \]