matrix multiplication is commutative

Matrix multiplication is not commutative in general. Matrix multiplication is associative i.e., (AB)C = A(BC), whenever both sides are defined. Matrix multiplication is distributive over matrix addition i.e., ..

This means that A + B = B + A, where A, B are 2 matrices of the same orde..

When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by ..

Let A=[a i j ] be an m x n matrix and k be any number called a scalar. Then the matrix obtained by multiplying every element of A by k is called the scalar multiple of A by k and is denoted by kA. Thus, kA = [k a i j ] m x ..

When a matrix is multiplied by a scalar factor k, then each element of the matrix is multiplied by ..

Two matrices A and B can be multiplied if the number of columns of A is equal to the number of rows of B. The resultant matrix will be of the order of (number of rows of A x number of columns of B). If A be a matrix of the order m x n and B be a matrix of t..

Let A be a matrix of order mxn. Let B be a matrix of order nxp. Then the product of the matrices A and B is of order mxp. i.e., when we multiply two matrices the number of columns of the first matrix should be equal to the number of rows of the second matrix..

Let us consider the sales done by a school canteen for two successive days. Monday 25 cokes 12 cakes Tuesday 40 cokes 7 cakes Each coke costs $ 5 and cake costs $ 10. The sales can be expressed as a 2 x 2 matrix and the price as a 2 x 1 matrix as given below: The amount collecte..

What are the values of a and b in the equation 4.23 × 2.41 = b × a , if the equation illustrates the commutative property of multiplication? => a = 4.23, b = 2.41 or a = 2.41, b = 4.23 or a = 8, b = 1.52 or a = 2.41, b = 8..

Use augmented matrices to find the multiplicative inverse of the matrix B = ( 5 1 - 1 0 ) . => ( - 5 - 1 1 0 ) or ( 1 0 0 1 ) or ( 0 - 1 1 5 ) or does not exist..