Which of the following statement are correct?
(A) $A = [a_{ij}]_{n×n}$ is a diagonal matrix if $a_{ij}=0$ when $i = j$
(B) A square matrix $A = [a_{ij}]$ is called a symmetric matrix if $a_{ij}=a_{ji}$ for all $i,j$
(C) A square matrix $A = [a_{ij}]$ is called a skew-symmetric matrix if $a_{ij}=-a_{ji}$ for all $i,j$
(D) For every square matrix A, there exist an identity matrix of the same order such that IA = AI= I
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (B) and (C) only
Check each statement:
(A) A = [aij] is a diagonal matrix if aij = 0 when i = j.
→ Incorrect, because for a diagonal matrix, aij = 0 when i ≠ j.
(B) A square matrix A = [aij] is called a symmetric matrix if aij = aji for all i, j.
→ Correct ✔
(C) A square matrix A = [aij] is called a skew-symmetric matrix if aij = −aji for all i, j.
→ Correct ✔
(D) For every square matrix A, there exist an identity matrix of the same order such that IA = AI= I. → Incorrect, because although an identity matrix, I always exists for a square matrix. The correct property is IA = AI= A
Correct statements: (B) and (C)