The matrix A has x rows and (x + 5) columns and the matrix B has y rows and (11 - y) columns. If both the matrices AB and BA exits, then the value of x and y are

Concept:

 A is a matrix of order m x n and  B is a matrix of order p x q

Where m is number of rows and n is number of column  of matrix A 

Similarly p is number of row and q is number of column of matrix B

For matrix multiplication to exist: Number of column of first matrix equal to number rows of second matrix

So for matrix multiplication AB , n = p

So for matrix multiplication BA , q = m

Calculation:

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