The matrix `A` has `x` rows and `(x+5)` column. If the matrix `B` has `y` rows and `(11-y)` columns `&` both `A Ba n dB A` exist, then `x=8` (b) `x=3` `y=6` (d) `y=8`

Options

A. 8 and 3
B. 3 and 4
C. 3 and 8
D. 8 and 8

Answer

C

Explanation

Given, Matrix A has x rows and x + 5 columns Matrix B has y row and 11 - y columns.
Also given AB and BA exists.
If AB exists, then the number of rows in A most be equal to number of columns in B.
i.e., `x = 11 - y" "...(1)`
If BA exists, then the number of rows in B must be equal to number of rows in A.
i.e., x + 5 = y
`rArr 11-y+5=y` (from (1))
`rArr 2y = 16`
`rArr y = 8`.
`(1) rArr x = 11 - 8 = 3`.
So, `x = 3, y = 8`.