Question

Matrix A has x rows and x + 5 columns. Matrix B has y rows and 11 - y columns. Both AB and BA exist.Then, the value of x and y is equal to

• A. 3, 9
• B. 8, 3
• C. 3, 8
• D. 4, 8

Answer 1

The correct option is C

3, 8

Since, AB is defined, number of rows in A = number of column in B

$\Rightarrow$ x = 11 - y or x + y = 11 .......... (i)​

Also, BA is defined,

So that number of rows in B = number of columns in A

$\Rightarrow$ x + 5 = y or x - y = -5 .................. (ii)​

From Eqs. (i) and (ii), we find that x = 3, y = 8

Hence, (c) is the correct answer.