Question

If AB=C where A is a matrix of order 2×4 and C is a matrix of order 2×5 then the order of B​

Answer 1

Answer:

4 × 5

Step-by-step explanation:

the product of matrices A & B is possible if number of columns of A = number of rows of B

hence....

A * B = C

(2 × 4 ) * ( m × n ) = 2 × 5

therefore m= 4 ; n = 5

B : ( 4 × 5 )

Answer 2

Order of matrix $B$ is  $4\times 5$

Step-by-step explanation:

Given,

$AB=C$ where $A$ is a matrix of order $2\times 4$ and $C$ is a matrix of order $2\times 5$

∴ $AB=C$

Multiply $A^{-1}$ both sides,

⇒ $A^{-1} AB=CA^{-1}$

⇒$IB=CA^{-1}$  Where $AA^{-1}=I$ and $I=$Unit vector.

⇒ $B=CA^{-1}$  Where $IB=B$

Order of $A$ is $2\times 4$

∴ Order of $A^{-1}$ is $4\times 2$

And Order of $C$ is $2\times 5$

⇒$B=(4\times 2)(2\times 5)$

⇒$B=4\times 5$

So, Order of matrix $B$ is  $4\times 5$