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:
Answer & explanation
Correct answer: option 2
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)