Matrix subtraction is an operation to find the difference between two matrices. Just like matrix addition, the subtraction operation can only be performed if both matrices involved have the same size or order.
The result of matrix subtraction is a new matrix that also has the same order, where each element is the result of subtracting the corresponding elements from the two initial matrices.
Ensure Same Order: The first and most important step is to check if both matrices have the same number of rows and columns. If their orders are different, subtraction cannot be performed.
Subtract Corresponding Elements: If the orders are the same, subtract each element of the second matrix (subtrahend) from the corresponding element of the first matrix.
Form the Resultant Matrix: Arrange the results of these subtractions into a new matrix. This new matrix will have the same order as the initial matrices.
Suppose matrix K=1−23051 and matrix L=[4027].
Matrix K is of order 3×2, while matrix L is of order 2×2. Since the orders of these two matrices are different, the subtraction K−L (or L−K) cannot be performed or is undefined.
Unlike matrix addition, which has several important properties like commutativity and associativity, matrix subtraction generally does not possess these properties.
Not Commutative: In general, the order of matrix subtraction significantly affects the result. This means A−B is not equal to B−A, except in special cases (e.g., if A=B).
A−B=B−A(in general)
For example, from matrices P and Q above:
P−Q=[6443]
Whereas,
Q−P=[2−114]−[8357]
It is clear that P−Q=Q−P.
Not Associative: The grouping in the subtraction of three or more matrices also affects the final result. In general, (A−B)−C is not equal to A−(B−C).
(A−B)−C=A−(B−C)(in general)
The only "property" important to remember is its relationship with addition, i.e., A−B=A+(−B).
By converting subtraction into addition with the opposite matrix, we can use addition properties when needed.
