Matrix multiplication is the most useful matrix operation. It is widely used in areas such as network theory, transformation of coordinates and many more uses nowadays. A matrix in R can be created using ** matrix()** function and this function takes input vector, nrow, ncol, byrow, dimnames as arguments.

**Creating a matrix**

A matrix can be created using matrix() function.

`# R program to create a matrix` `m <` `-` `matrix(` `1` `:` `8` `, nrow` `=` `2` `)` `print` `(m) ` |

**Output:**

[,1] [,2] [,3] [,4] [1,] 1 3 5 7 [2,] 2 4 6 8

#### Multiplication of Matrices

The multiplication operator ***** is used for multiplying a matrix by scalar or element-wise multiplication of two matrices.

**Multilication with scalar**

If you multiply a matrix with a scalar value, then every element of the matrix will be multiplied with that scalar.**Example:**

`# R program for matrix multiplication` `# with a scalar` `m <` `-` `matrix(` `1` `:` `8` `, nrow` `=` `2` `)` `m <` `-` `2` `*` `m ` `print` `(m)` |

**Output:**

[,1] [,2] [,3] [,4] [1,] 2 6 10 14 [2,] 4 8 12 16

In the above code, the scalar is multiplied with every element of the original matrix. This is how the multiplication process takes place:

2*1=2 2*3=6 2*5=10 2*7=14 2*2=4 2*4=8 2*6=12 2*8=16

**Multiplication between Matrices**

When a matrix is multiplied with another matrix, the element-wise multiplication of two matrices take place. All the corresponding elements of both matrices will be multiplied under the condition that both matrices will be of the same dimension.**Example:**

`# R program for matrix multiplication` ` ` `# Creating matrices` `m <` `-` `matrix(` `1` `:` `8` `, nrow` `=` `2` `)` `n <` `-` `matrix(` `8` `:` `15` `, nrow` `=` `2` `)` ` ` `# Multiplying matrices` `print` `(m` `*` `n)` |

**Output:**

[,1] [,2] [,3] [,4] [1,] 8 30 60 98 [2,] 18 44 78 120

This is how the multiplication process takes place:

1*8=8 3*10=30 5*12=60 7*14=98 2*9=18 4*11=44 6*13=78 8*15=120

**Multiplication with Vector**

If a matrix is multiplied with a vector then vector will be promoted to either row or column matrix to make two arguments conformable.**Example:**

`# R program for matrix multiplication` ` ` `# Creating matrix` `m <` `-` `matrix(` `1` `:` `8` `, nrow` `=` `2` `) ` ` ` `# Creating a vector` `vec <` `-` `1` `:` `2` ` ` `# Multiplying matrix with vector` `print` `(vec` `*` `m)` |

**Output:**

[,1] [,2] [,3] [,4] [1,] 1 3 5 7 [2,] 4 8 12 16

This is how the multiplication process takes place:

1*1=1 1*3=3 1*5=5 1*7=7 2*2=4 2*4=8 2*6=12 2*8=16

**Multiplication using %*% operator**

The Operator**%*%** is used for matrix multiplication satisfying the condition that the number of columns in the first matrix is equal to the number of rows in second. If matrix A[M, N] and matrix B[N, Z] are multiplied then the resultant matrix will of dimension M*N.**Example:**

`# R program for matrix multiplication` ` ` `# Creating matrices` `m <` `-` `matrix(` `1` `:` `8` `, nrow` `=` `2` `)` `n <` `-` `matrix(` `8` `:` `15` `, nrow` `=` `4` `)` ` ` `# Multiplying matrices using operator` `print` `(m ` `%` `*` `%` `n)` |

**Output:**

[,1] [,2] [1,] 162 226 [2,] 200 280

This is how multiplication takes place:

1*8+3*9+5*10+7*11 = 162 1*12+3*13+5*14+7*15=226 2*8+4*9+6*10+8*11 = 200 2*12+4*13+6*14+8*15=280

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