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?

Answer 1

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