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

• 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 columns in A = number of rows in B

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

Also, BA is defined,

Number of columns in B = number of rows in A

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

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