Which of the following statement is/are correct?
(A) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij}=a_{ji}$ for all $i,j$
(B) $A = [a_{ij}]_{m×m}$ is a diagonal matrix if $a_{ij} =0$ when $i = j$
(C) A square matrix $A = [a_{ij}]$ is called a skew symmetric matrix, if $a_{ij} = -a_{ji}$ for all $i,j$
(D) The multiplication of diagonal matrices of same order is commutative
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
(A) A square matrix $A = [a_{ij}]$ is called symmetric if $a_{ij} = a_{ji}$ for all $i,j$ — ✔ True
(B) A matrix is diagonal if $a_{ij} = 0$ when $i = j$ — ✖ False (It should be $a_{ij} = 0$ when $i \ne j$)
(C) A square matrix $A = [a_{ij}]$ is skew-symmetric if $a_{ij} = -a_{ji}$ for all $i,j$ — ✔ True
(D) The multiplication of diagonal matrices of the same order is commutative — ✔ True (Since diagonal entries multiply element-wise)
Final Answer:
(A), (C), and (D)