Question

Find the output order for the following matrix multiplication $A_{4\times 2}\times B_{2\times 4}$?

• A. $2\times 4$
• B. $4\times 4$
• C. $4\times 2$
• D. Multiplication not possible

Answer 1

The correct option is B $4\times 4$

Note:

1. $m\times n$ is the order of matrix $AB$ if the order of matrix $A$ is $m\times p$ and the order of $B$ is $p\times n$.

2. For matrix multiplication to work, the columns of the second matrix have to have the same number of entries as do the rows of the first matrix.

Here $A,B$ are conformant matrices, Multiplication is possible.
Therefore, $A$ is of size $4\times 2$, and $B$ is of size $2\times 4$, in which case the output is of size $4\times 4$ and is the matrix product of $A$ and $B$.