How to Multiply Matrices?
Suppose we have to find the multiplication of two matrices A and B where the number of columns in A is equal to the number of rows in B such that the multiplication of A and B is obtained in such a way that we multiply the first row of the first matrix with the first column of the second matrix to get the first element of the multiplied matrix.
We follow the steps discussed below to find the matrix multiplication.
Step 1: Check the compatibility of the matrix by checking that the number of columns in the 1st matrix equals the number of rows in the 2nd matrix.
Step 2: Multiply the elements in the first row of the first matrix with the elements in the first column of the matrix and find the sum of all the products.
Then multiply the element in the first row of the first matrix with the elements of the second column in the second matrix. Repeat this process till elements of all the positions are not obtained.
Step 3: Substitute all the elements obtained in Step 2 in their respective position to find the required product matrix.
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