Let A, B, C, D and E be matrices of order $2 × n,3 × k, 2× p,n × 3$ and $p × k$ respectively. Choose the correct statement(s) from the following?

(A) EB + DB will be defined if $k = 3, p = n$.
(B) EB + DB will be defined if $k = 2, p = 3$.
(C) If $n = p = 2$, then the order of the matrix $5A^2 - 3C$ is $2 × 2$.
(D) If $n = p$, then the order of the matrix $5A^2 - 3C$ is $p ×k$.

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is Option (2) → (A) and (C) only

Orders are

$A:2\times n,\; B:3\times k,\; C:2\times p,\; D:n\times3,\; E:p\times k$

(A) $EB$ is defined when $k=3$ and $DB$ is defined when $p=n$.

Then both $EB$ and $DB$ have same order $p\times k$.

So (A) is correct.

(B) If $k=2,p=3$ then $EB$ is $3\times2$ but $DB$ is not defined.

So (B) is false.

(C) If $n=p=2$, then $A$ is $2\times2$ and $C$ is $2\times2$.

So $5A^2-3C$ has order $2\times2$.

So (C) is correct.

(D) If $n=p$, then $A$ is $2\times p$ so $A^2$ is not defined.

So (D) is false.

Correct statements are (A) and (C)