Answer
True.
Work Step by Step
A matrix of order $m\times n$ has $m$ rows and $n$ columns
See p.618, Matrix Multiplication:
The product of an $m\times n$ matrix $A$ and an $n\times p$ matrix $B$ is an $m\times p$ matrix $AB$.
n= number of columns in A = number of rows in B.
For example, a 2$\times$3 matrix and a 3$\times$4 matrix can be multiplied, and they do not have same orders.
(number of columns in a 2$\times$3 matrix = 3 = number of rows in a 3$\times$4 matrix .)
True.