A has ‘a’ rows and ‘a + 3’ columns. B has‘b’ rows and ‘17–b’ columns, and if bothproducts AB and BA exist, find a, b?

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?

Match the items on the right to the items on the left.

STEP 1

STEP 2

STEP 3

STEP 4

STEP 5

Given Order of A is a × (a + 3)
Order of B is b × (17 − b)
Product AB exist

⇒ a + 3 = b
(No. of columns in A = No. of rows in B)
⇒ a − b = − 3 ........ (1)
Product BA exist

⇒ 17 − b = a
(No. of columns in B = No. of rows in A)
⇒ a + b = 17 ........ (2)

Solving (1) & (2)
2a = 14
a = 7
Sub a = 7 in (1)

7 − b = − 3
b = 10
∴ a = 7, b = 10