Question

	LIST I (Type of the Matrix)		LIST II (Property)
A.	Symmetric Matrix		I. aij = aji, for values of i and j
B.	Hermitian Matrix		II. aij = āji, for values of i and j
C.	Skew-Hermitian matrix		III. aij = -āji, for values of i and j
D.	Skew-Symmetric matrix		IV. aij = -aji, for values of i and j

Choose the correct answer from the options given below:

• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (I), (B) - (III), (C) - (II), (D) - (IV)
• (A) - (II), (B) - (I), (C) - (IV), (D) - (III)
• (A) - (II), (B) - (III), (C) - (IV), (D) - (I)

Hint:

Symmetric matrices satisfy aij = aji, while skew-symmetric matrices satisfy aij = −aji.

Answer 1

The Correct Option is D

Symmetric matrices have \( a_{ij} = a_{ji} \).
Hermitian matrices have the same property as symmetric matrices, but they also have complex entries
Skew-Hermitian matrices have \( a_{ij} = -a_{ji} \).
Skew-Symmetric matrices also have \( a_{ij} = -a_{ji} \), but are specifically real matrices.