Question

The matrix A has $x$ rows and $x+5$ columns. The matrix $B$ has $y$ rows and $11-y$ columns. Both $AB$ and $BA$ exist. What are the values of $x$ and $y$ respectively?

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

Answer 1

The correct option is C $3$ and $8$

Given matrix $A$ has $x$ rows and $x+5$ columns.The matrix $B$ has $y$ rows and $11-y$ columns and also $AB$ and $BA$ exist,

$\therefore$ number of columns of $A$ is equal to number of rows of $B$,

$⟹x+5=y$,

and also number of columns of $B$ is equal to number of rows of $A$,

$⟹x=11-y$,

Solving the both linear equations gives,

$y=8$ and $x=3$

Hence, the answer is $3$ and $8$.