Let A and B be two non zero square matrices and AB and BA both are defined. It means
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both matrices (A) and (B) have same order
Let A be of order m × n and B of order p × q. A product is defined only when the number of columns of the first matrix equals the number of rows of the second:
\(AB \text{ defined} \Rightarrow n = p\)
\(BA \text{ defined} \Rightarrow q = m\)
Both matrices are square, so m = n and p = q. Then
\(m = n = p = q\)
So A and B have the same order.
Why the other options are incorrect
Option (1) No. of columns of A ≠ No. of rows of B — Incorrect. AB is defined, so these two numbers are equal.
Option (2) No. of rows of A ≠ No. of columns of B — Incorrect. BA is defined, so these two numbers are equal.
Option (4) Both matrices (A) and (B) does not have same order — Incorrect. m = n = p = q, so the orders are the same.