# Manuals/calci/MATRIXPRODUCT

**MATRIXPRODUCT (a,b,ConsiderUnits)**

- where and are the array of two matrices

## Description

- This function gives product of two matrices.
- Matrix multiplication is of two types:

Type 1: A scalar (a constant) is multiplied with the each element of the matrix. Type 2: Multiplication of two matrices.

- We can do the matrix multiplication when the number of columns in the first matrix equals the number of rows in the second matrix.
- For e.g. 4x2 matrix can multiply with 2x3. The matrix product of two arrays and is: where is the row number and is the column number.
- i.e Multiply the elements of each row of 1st matrix by elements of each column of 2nd matrix.
- So the resultant matrix is of the order: Rows of 1st matrix × Columns of 2nd.
- For e.g If we multiply a 4x2 matrix with a 2x3 matrix, the product matrix is of order 4x3.
- Matrix multiplication satisfies the associative and distributive properties.But it is not satisfies the commutative property.
- i.e., Let A,B and C are three matrices, then A(BC)= (AB)C (Associative property)
- A(B+C)= AB+AC and (A+B)C = AC+BC (Distributive properties)
- k(AB)=(kA)B=A(kB)where k is a constant.But (Commutative property)

## Examples

1. MATRIXPRODUCT([2,3,4;5,6,7],5)

10 | 15 | 20 |

25 | 30 | 35 |

2. MATRIXPRODUCT([[6,7,8],[10,12,-22],[7,17,23]],[[20,12,16],[7,8,13],[4,8,9]])

120 | 84 | 128 |

70 | 96 | -286 |

28 | 136 | 207 |

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## See Also

## References