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Question
A has ‘a’ rows and ‘a + 3’ columns. B has ‘b’ rows and ‘17 − b’ columns, and if both products AB and BA exist, find a, b?
Solution
Order of A = a × (a + 3)
Order of B = b × (17 – b)
Given: Product of AB exist
a + 3 = b
a – b = – 3 ….(1)
Product of BA exist
17 – b = a
– a – b = – 17
a + b = 17 ………(2)
(1) + (2) ⇒ 2a = 14
a = `14/2` = 7
Substitute the value of a = 7 in (1)
7 – b = – 3 ⇒ – b = – 3 – 7
– b = – 10 ⇒ b = 10
The value of a = 7 and b = 10
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