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MATRIXPRODUCT (a,b,ConsiderUnits)

  • where and are the array of two matrices


  • 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)


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

See Also


Matrix Multiplication