If A and B are two matrices of the order 3 × m and 3 × n, respectively, and m = n, then the order of matrix (5A – 2B) is

The correct option is 3 × n.

Let's understand why this is the correct answer step-by-step.

Step 1: Understanding Matrix Operations (Addition and Subtraction)
For any two matrices to be added or subtracted, they must have the exact same dimensions (or order). That is, if matrix $X$ and matrix $Y$ are to be added ($X+Y$) or subtracted ($X-Y$), the number of rows in $X$ must equal the number of rows in $Y$, and the number of columns in $X$ must equal the number of columns in $Y$. The resulting matrix will also have this same order.

Step 2: Scalar Multiplication
Multiplying a matrix by a constant (scalar) does not change its order.
The matrix $5A$ has the same order as matrix $A$, which is $3\times m$.
Similarly, the matrix $2B$ has the same order as matrix $B$, which is $3\times n$.

Step 3: Finding the Order of (5A – 2B)
We are given that $m=n$.
Since $m=n$, the order of matrix $A$ ($3\times m$) is identical to the order of matrix $B$ ($3\times n$). Therefore, the subtraction operation $5A-2B$ is defined, and the resulting matrix will have the same order as that of both $A$ and $B$.

Thus, the order of the matrix $(5A-2B)$ can be written as either $3\times m$ or $3\times n$.
Matching this with the given options, we find 3 × n listed as a choice.