Question

If (AB)′ = B′ A′, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

Options

• True

• False

Answer 1

This statement is True.

Explanation:

Let A = `["a"_"ij"]_("m" xx "n")` and B = `["b"_"ij"]_("p" xx "q")`

AB is defined when n = P

∴ Order of AB = m × q

⇒ Order of (AB)' = q × m

Order of B' is q × p and order of A' is n × m

∴ B'A' is defined when P = n

And the order of B'A' is q × m

Hence, order of (AB)' = Order of B'A' i.e., q × m