You can use the following syntax to perform matrix multiplication in R:

#perform element-by-element multiplication A * B #perform matrix multiplication A %*% B

The following examples show how to use this syntax in practice.

**Example 1: Element-by-Element Multiplication**

The following code shows how to perform element-by-element multiplication between two matrices in R:

#define matrix A A <- matrix(c(1, 2, 3, 4), ncol=2) A [,1] [,2] [1,] 1 3 [2,] 2 4 #define matrix B B <- matrix(c(5, 6, 7, 8), ncol=2) B [,1] [,2] [1,] 5 7 [2,] 6 8 #perform element-by-element multiplication A*B [,1] [,2] [1,] 5 21 [2,] 12 32

Using the ***** operator, R simply multiplied the corresponding elements in each matrix to produce a new matrix.

Here are the exact calculations that were performed:

- Position [1, 1]: 1 * 5 =
**5** - Position [1, 2]: 3 * 7 =
**21** - Position [2, 1]: 2 * 6 =
**12** - Position [2, 2]: 4 * 8 =
**32**

**Example 2: Matrix Multiplication**

The following code shows how to perform matrix multiplication between two matrices in R:

#define matrix A A <- matrix(c(1, 2, 3, 4), ncol=2) A [,1] [,2] [1,] 1 3 [2,] 2 4 #define matrix B B <- matrix(c(5, 6, 7, 8), ncol=2) B [,1] [,2] [1,] 5 7 [2,] 6 8 #perform matrix multiplication A %*% B [,1] [,2] [1,] 23 31 [2,] 34 46

Here are the exact calculations that were performed:

- Position [1, 1]: 1*5 + 3*6 =
**23** - Position [1, 2]: 1*7 + 3*8 =
**31** - Position [2, 1]: 2*5 + 4*6 =
**34** - Position [2, 2]: 2*7 + 4*8 =
**46**

Refer to these tutorials for a quick primer on the formulas to use to perform matrix multiplication between matrices of various sizes:

- Matrix Multiplication: (2×2) by (2×2)
- Matrix Multiplication: (2×2) by (2×3)
- Matrix Multiplication: (3×3) by (3×2)

**Additional Resources**

How to Convert Matrix to Vector in R

How to Plot the Rows of a Matrix in R

very very useful