UPSC NDA Math Model Paper 5

Given
Matrix A
number of rows(m) = x
number of column(n) = x + 5
Matrix B
number of rows(p) = y
number of column(q) = 11 - y
Both AB and BA exists
n = p ⇒ x + 5 = y ....(1)
m = q ⇒11 - y = x ....(2)
put the value of y from 1 in 2
11-(x + 5) = x
11 - 5 - x = x
6 = 2 x
∴ x = 3
from 1 putting x=3
y = 8
∴ x = 3 and y = 8