# Manuals/calci/MATRIXPRODUCT

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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