102 LearnersLast updated on July 15th, 2025
Subtraction of Matrices
A matrix is a rectangular arrangement of numbers or expressions arranged into rows and columns. Subtraction of matrices is the process of subtracting corresponding elements of two or more matrices. In this topic, we will learn about the subtraction of matrices and their properties.
What is Subtraction of Matrices
Matrix subtraction is the process of subtracting the corresponding elements of two matrices of the same dimensions. For subtracting matrices, both matrices should have the same dimensions; that is, if matrix A is in m × n dimensions, then matrix B should also be in m × n dimensions.
Methods for Subtraction of Matrices
Matrix subtraction is the process of subtracting two matrices that have the same dimension. A matrix with ‘m’ rows and ‘n’ columns, then the dimension of the matrix is m × n. To subtract two matrices A and B of the same size, you subtract their corresponding elements. It is represented as (A - B)ij = Aij - Bij, where Aij and Bij are the elements in the matrix in the i-th row and j-th column. Let’s learn the Subtraction of Matrices of Order 2 × 2 and Order 3 × 3
Method 1: Subtraction of Matrices of Order 2 × 2
The matrix, of order 2 × 2, has 2 rows and 2 columns. For example, when subtracting matrix A and B of order 2 × 2, it can be represented as:
For example, subtracting A = [37 64] and B = [52 21]
A - B = [37 64] - [52 21]
= [3 - 57 - 2 6 - 24 - 1 ]
= [-2 5 43]
Method 1: Subtraction of Matrices of Order 2 × 2
The matrix, of order 2 × 2, has 2 rows and 2 columns. For example, when subtracting matrix A and B of order 2 × 2, it can be represented as:
For example, subtracting A = [37 64] and B = [52 21]
A - B = [37 64] - [52 21]
= [3 - 57 - 2 6 - 24 - 1 ]
= [-2 5 43]
Method 2: Subtraction of Matrices of Order 3 × 3
The subtraction of matrices involves a 3 × 3 order, that is, each of the matrices has 3 rows and 3 columns. Here, each corresponding element of one matrix from the other is subtracted. The subtraction of matrices of order 3 × 3 can be represented as:
For example, subtracting the matrices P and Q
Properties of Subtraction of Matrices
Like subtraction with numbers, matrices also follow certain properties. Here are some properties of the subtraction of matrices.
- The number of rows and columns in the given matrices should be the same when subtracting the matrices.
- The subtraction of matrices is not commutative and associative, that is, A - B ≠ B - A, and (A - B) - C ≠ A - (B - C), as the order of the element-wise subtraction.
- When subtracting a matrix from itself results in a zero matrix, that is, A - A = 0.
- The difference between two matrices is equal to the sum of adding the negative matrix to another, that is A - B = A + (-B).
Tips and Tricks for Subtraction of Matrices
We use matrix subtraction in the fields of engineering, physics, computer graphics, etc. So, students need to master the subtraction of matrices, and here are some tips and tricks to master the subtraction of matrices.
- Always check whether the dimensions of both matrices are the same or not because the dimensions of both matrices should be the same.
- In matrix subtraction, we subtract each element in the second matrix from the corresponding element in the first matrix.
- To master matrix subtraction, it is important to practice regularly.
Common Mistakes and How to Avoid Them in Subtraction of Matrices
When doing the subtraction of matrices, students make mistakes, which can result in errors. Here are some common mistakes and the ways to avoid them
Mistake 1
Subtracting matrices of different dimensions
Students sometimes try to subtract matrices with different dimensions, for example, subtracting a 2 × 3 matrix and a 3 × 2 matrix. So, students should remember that when subtracting matrices, they should have the same dimensions, that is, the number of rows and columns of both matrices should be the same.
Mistake 2
Confusing subtracting with addition
Students sometimes add the matrices instead of subtracting them, either by misreading the questions and confusing them with the operation sign. So always read the questions carefully and then always verify the operation sign.
Mistake 3
Subtracting the elements in the wrong order
One common mistake that students make when subtracting matrices is subtracting the elements in the wrong order.
For example, when subtracting matrix B from matrix A, A = [a 21a 11 a 22a 12] and B = [b 21b 11 b 22b 12], students incorrectly subtract element b12 from a11 instead of subtracting b12 from a12. To avoid this error, always ensure that you subtract the corresponding elements.
Mistake 4
Errors while subtracting negative numbers
When subtracting negative numbers in matrix elements, students make errors.
For example, 4 - (-2) as 2 instead of 6. So when subtracting negative numbers, students should remember that a - (-b) = a + b and always try to verify the answer.
Mistake 5
Assuming matrix subtraction is commutative
Students assume that A - B = B - A, but it’s wrong, as matrix subtraction is not commutative. In other words, the order of the matrix is specific for subtraction. So, always follow the order when subtracting the matrix.
Examples of Subtraction of Matrices
Problem 1
Explanation
Problem 2
Explanation
Problem 3
Explanation
Problem 4
Explanation
Problem 5
Explanation
FAQs on Subtraction of Matrices
1.What is the subtraction of matrices?
2.Can you subtract a 3 × 2 and a 2 × 3 matrix?
3.Is matrix subtraction commutative?
4. What is the result of subtraction a matrix from itself?
5.Is matrix subtraction associative?
6.How can children in United States use numbers in everyday life to understand Subtraction of Matrices?
7.What are some fun ways kids in United States can practice Subtraction of Matrices with numbers?
8.What role do numbers and Subtraction of Matrices play in helping children in United States develop problem-solving skills?
9.How can families in United States create number-rich environments to improve Subtraction of Matrices skills?
Important Glossaries for Subtraction of Matrices
- Matrix: The way of arranging numbers in columns and rows in a rectangular array is called a matrix.
- Order of a matrix: The order of a matrix is the number of rows and columns in the matrix. It is the dimension of the matrix written in the form m × n, where m is the number of rows and n is the number of columns.
- Subtraction: Subtraction is a basic mathematical operation of finding the difference between two or more numbers. For example, 5 -2 = 3.
