NIMCET 2016 — Mathematics PYQ

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 columns $(n)=x+5$  

**Matrix B**  
number of rows $(p)=y$  
number of columns $(q)=11-y$  

Both $AB$ and $BA$ exist  

$n=p\Rightarrow x+5=y...(1)$  
$m=q\Rightarrow 11-y=x...(2)$  

Put the value of $y$ from (1) into (2):  
$11-(x+5)=x$  

$11-5-x=x$  

$6=2x$  

$\therefore x=3$  

From (1), putting $x=3$:  
$y=8$  

$\therefore x=3\text{ and }y=8$