## R – Matrix Multiplication

To perform matrix multiplication in R, use the multiplication operator `%*%`. Please note the percentile `%` symbols surrounding the arithmetic multiplication operator `*`.

In this tutorial, we will learn how to multiply matrices using Matrix Multiplication operator with the help of examples.

### Syntax

The syntax of the expression to multiply matrices `A` and `B` is

`A %*% B`

The expression returns a matrix. The number of columns in matrix `A` must equal the number of rows in matrix `B`.

### Examples

In the following program, we will create matrices `A` and `B`; multiply them using the matrix multiplication operator, and store the result in matrix `AB`.

example.R

```data <- c(1, 2, 3, 0, 1, 2, 0, 0, 1)
A <- matrix(data, nrow = 3, ncol = 3)

data <- c(0, 1, 1, 1, 0, 3, 1, 3, 3)
B <- matrix(data, nrow = 3, ncol = 3)

AB <- A %*% B

print("Matrix A")
print(A)
print("Matrix B")
print(B)
print("Matrix Multiplication Result")
print(AB)```

Output

``` "Matrix A"
[,1] [,2] [,3]
[1,]    1    0    0
[2,]    2    1    0
[3,]    3    2    1
 "Matrix B"
[,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    0    3
[3,]    1    3    3
 "Matrix Multiplication Result"
[,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    2    5
[3,]    3    6   12```

Matrix Multiplication operator can be chained. Therefore, we can multiply multiple matrices in a single expression.

Now, let us take three matrices: `A`, `B` and `C`; and find their product `ABC`.

example.R

```data <- c(1, 2, 3, 0, 1, 2, 0, 0, 1)
A <- matrix(data, nrow = 3, ncol = 3)

data <- c(0, 1, 1, 1, 0, 3, 1, 3, 3)
B <- matrix(data, nrow = 3, ncol = 3)

data <- c(1, 1, 0, 1, 0, 0, 1, 0, 1)
C <- matrix(data, nrow = 3, ncol = 3)

AB <- A %*% B %*% C

print("Matrix A")
print(A)
print("Matrix B")
print(B)
print("Matrix C")
print(C)
print("Matrix Multiplication Result")
print(AB)```

Output

``` "Matrix A"
[,1] [,2] [,3]
[1,]    1    0    0
[2,]    2    1    0
[3,]    3    2    1
 "Matrix B"
[,1] [,2] [,3]
[1,]    0    1    1
[2,]    1    0    3
[3,]    1    3    3
 "Matrix C"
[,1] [,2] [,3]
[1,]    1    1    1
[2,]    1    0    0
[3,]    0    0    1
 "Matrix Multiplication Result"
[,1] [,2] [,3]
[1,]    1    0    1
[2,]    3    1    6
[3,]    9    3   15```

### Conclusion

In this R Tutorial, we learned how to perform Matrix Multiplication in R, with the help of examples.