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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
Solution
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
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