Question

Let $A_{3\times 4},B_{4\times 5},C_{5\times 1}$ and $D_{1\times 4}$ be the matrices. Then which of the following is true

• A. Order of $\left(ABCD\right)$ is $3\times 4$
• B. Order of $\left(ABCD\right)$ is $4\times 3$
• C. Order of $\left(ABCD\right)$ is $4\times 4$
• D. Order of $\left(ABCD\right)$ can not be determined

Answer 1

The correct option is A Order of $\left(ABCD\right)$ is $3\times 4$

$AB$ exists
$(\because$ number of columns of $A=$ number of rows of $B$)
$\therefore A_{3\times 4},B_{4\times 5}\Rightarrow (AB{)}_{3\times 5}$

$ABC$ exists
$(\because$ number of columns of $AB=$ number of rows of $C$)
$\therefore (AB{)}_{3\times 5},C_{5\times 1}\Rightarrow (ABC{)}_{3\times 1}$

$ABCD$ exists
$(\because$ number of columns of $ABC=$ number of rows of $D$)
$\therefore (ABC{)}_{3\times 1},D_{1\times 4}\Rightarrow (ABCD{)}_{3\times 4}$