What does it mean if matrices AB BA?
In general, AB = BA, even if A and B are both square. If AB = BA, then we say that A and B commute. • For a general matrix A, we cannot say that AB = AC yields B = C. (However, if we know that A is invertible, then we can multiply both sides of the equation AB = AC to the left by A−1 and get B = C.)
What is the necessary condition for the product AB BA if the matrices A and B to be both defined and to be both equal?
From (4) and (5), we can conclude that A and B are square matrices and their orders are one and the same. Thus, for both addition and multiplication of two matrices to be possible, it is required that both the matrices should be of same order and they should be square matrices.
What does B mean in matrices?
B = By convention, matrices in text are printed in bold face. Elements (entries) of the matrix are referred to by the name of the matrix in lower case with a given row and column (again, row comes first). For example, a31 = 2, b22=1. In general, aij means the element of A in the ith row and jth column.
When product of two matrices A and B is defined?
The product of two matrices A and B is defined if the number of columns of matrix A is equal to number of rows of matrix B.
Under what condition two matrices A and B are conformable for the product AB also what will be the order of AB?
(c) Product of Matrices: Two matrices A and B are said to be conformable for the product AB if the number of columns of A is equal to the number of rows of B.
Is A and B are two matrices such that both a B and AB are defined then?
A and B are of same order. Obviously, both simultaneously mean that the matrices A and B are square matrices of same order.
How do you prove AB BA in a matrix?
Need to show: AB = BA. Since A is not square, m = n. Therefore, the number of rows of AB is not equal to the number of rows of BA, and hence AB = BA, as required.
Is a b = b a a square matrix?
First of all, note that if A B = B A, then A and B are both square matrices, otherwise A B and B A have different sizes, and thus wouldn’t be equal.
What is the product of A and B in the matrix?
Since A is 2 x 3 and B is 3 x 4, the product AB, in that order, is defined, and the size of the product matrix AB will be 2 x 4. The product BA is not defined, since the first factor (B) has 4 columns but the second factor (A) has only 2 rows.
What is the Order of transformation A and B in matrix A?
Matrix A is ( − 1 0 0 − 1) and matrix B is ( 1 0 0 − 1). B A = ( 1 0 0 − 1) ( − 1 0 0 − 1) = ( − 1 0 0 1). A B = ( − 1 0 0 − 1) ( 1 0 0 − 1) = ( − 1 0 0 1). Thus A B = B A, and thus the order in which the two transformations A and B are applied does not matter.
When do the two matrices commute?
When the two matrices are simultaneously diagonalizable then the matrices commute. i.e. if $A=P\\Lambda P^ op$, $B=P\\Sigma P^ op$ with $P$ an orthogonal matrix and $\\Sigma$, $\\Lambda$ diagonal matrices then $AB=BA$.