Suppose that A, B and C are matrices of order $m×n,n×5$ and $5×q$ respectively. The restriction on $m,n$ and $q$ so that AB-BC is defined are

$m = n,q = 5$

The correct answer is Option (2) → $m = n,q = 5$

Given matrices:

$A$ is of order $m \times n$

$B$ is of order $n \times 5$

$C$ is of order $5 \times q$

To define $AB$, the number of columns of $A$ must equal the number of rows of $B$.

That is already satisfied ($n$ = $n$). So,

$AB$ is of order $m \times 5$.

Now, $BC$ is defined since $B$ ($n \times 5$) and $C$ ($5 \times q$) are conformable.

Thus, $BC$ is of order $n \times q$.

For $AB - BC$ to be defined, both matrices must have the same order.

Hence, $m \times 5 = n \times q$

Therefore, the restriction is:

$m = n$ and $q = 5$