Q.Matrices of different order can not be subtracted.

Matrix subtraction is defined entry by entry: $(A-B)_{ij} = a_{ij} - b_{ij}$. For every entry to have a matching partner, both matrices must have the same number of rows and the same number of columns — i.e. the same order. If the orders differ, some positions have no counterpart and the operation is undefined (equivalently, $A - B = A + (-B)$ still needs the same order …

Why the order must match

Matrix subtraction is defined entry by entry. If $A$ and $B$ are matrices, their difference is formed by subtracting each element of $B$ from the element of $A$ in the same position:

For this rule to make sense, every position $(i,j)$ in $A$ must have a matching position $(i,j)$ in $B$. That happens only when the two matrices have the same number of rows and the same number of columns — that is, the same order.

What goes wrong when the orders differ

Suppose $A$ has order $m \times n$ and $B$ has order $p \times q$ with $m \neq p$ or $n \neq q$. Then there is at least one position that exists in one matrix but not in the other, so the entry-wise subtraction $a_{ij} - b_{ij}$ has no partner term to compute. The operation is therefore not defined. …

Method: Check whether matrix subtraction is defined

Use this to judge any statement about subtracting matrices.

Steps

Step 1: State the rule.

Subtraction, like addition, is defined only for matrices of the same order, and is done entry-by-entry: $A - B = [\,a_{ij} - b_{ij}\,]$.

Step 2: Apply it to the claim. …

Common Mistakes

Mistake 1: Thinking a matching total number of entries permits subtraction.

Why it's wrong: a $2\times3$ and $3\times2$ share $6$ entries but different positions, so subtraction is still undefined. Correct approach: demand the same order, not just the same entry count. …