What is Matrix Multiplication in Maths?
Matrix multiplication is the mathematical operation that is performed on two matrices which when multiplied gives a singular matrix.
Suppose we take two matrices A and B such that the number of columns in the first matrix is equal to the number of rows in the second matrix then we can multiply these two matrices to get a new matrix of the same order that is called the multiplication of the two matrices A and B.
Matrix Multiplication Definition
Matrix multiplication is an operation that takes two matrices and produces a third matrix. This product is calculated by taking the dot product of rows from the first matrix with columns of the second matrix.
If “A = [aij]m×n” and “B = [bij]n×p” are two matrices, then the product of A and B is denoted as AB, whose order is “m × p.” this condition is represented as,
Matrix multiplication is not commutative, i.e., AB ≠ BA, or, in simple words, the product of A and B matrices is AB and AB is not equal to BA it is even possible that AB exists but BA does not exist.
Note: French mathematician Jacques Philippe Marie Binet was the first to perform matrix multiplication in 1812.
Read in Detail: Matrices
Matrix Multiplication – How to Multiply Matrices, Methods, Examples
Matrix Multiplication is the product of two matrices that result in the formation of one matrix. It is a binary operation performed on two matrices to get a new matrix called the product matrix. Two matrices can only be multiplied if the number of columns of the first matrix is equal to the number of rows of the second matrix.
In this article, we will learn about Matrix Multiplication, How to Multiply Matrices, Rules for Matrix Multiplication, Examples of Matrix Multiplication, and others in detail.
Table of Content
- What is Matrix Multiplication in Maths?
- Matrix Multiplication Definition
- How to Multiply Matrices?
- What are the Matrix Multiplication Rules?
- Matrix Multiplication Notation
- Matrix Multiplication Formula
- Algorithm for Matrix Multiplication
- Matrix Multiplication Rules
- 2×2 Matrix Multiplication Formula
- 3×3 Matrix Multiplication Formula
- Matrix Multiplication by Scalar
- Properties of Matrix Multiplication
- Commutative Property
- Associative Property
- Distributive Property
- Product with a Scalar
- Determinant of Matrix Multiplication
- Transpose of Matrix Multiplication
- Multiplicative Identity Property
- Multiplicative Property of Zero
- Matrix Multiplication Examples
- Practice Problems on Matrix Multiplication