Question

1. A is a matrix of order 3 x 2 and B is a matrix having 6 elements. If the product
AB exists, then find the order of the matrix AB.​

Answer 1

Order of A= 3x2 = 3rows and 2columns
B has 6 elements means that the possible order could be any of the following:-
1) 3x2
2) 2x3
3) 1x6
4) 6x1
For multiplication to happen between 2 matrices its important that:-
number of rows of 1 matrice should= no. Of columns of 2 nd matrice ——(C)
As mentioned above A has 3 rows .
Therefore 3) and 4) cannot be possible
Thus only 1) and 2) are left:-
A: 3 rows and 2 columns (by order : 3 x2)
Therefore B must have: 2 rows and 3 columns (using C)
Thus correct order of B is 2x3
Final order of matrix after multiplication is always Rows of 1st matrix and columns of the other using this correct order of AB is 3x3.

Answer 2

Answer:

Matrix of Order

Step-by-step explanation:

• The matrix of order is a two dimensional matrix which mainly consists of the number of rows in m and the number of columns in n.
• The order of a matrix will be equal to be value:

        m x n

Formula of order of matrix:

Order of matrix = number of rows * number of columns

Types of different order of matrix. They are:

Order of  row matrix

Order of column matrix

Order of square matrix

Order of rectangular matrix

Order of transpose matrix

Given that:

Let the Matrix A is of order 3 x 2

B matrix having 6 elements

Product AB exists.

To find:

order of the matrix AB =?

Solution:

Here, Order of A = 3x2

(3 rows and 2 columns)

B is having 6 elements. So the possible order is:

   3x2

   1x6

   6x1

   2x3

• For multiplication of matrix, we know that,
• The number of rows of one matrix will be equal to the columns present in the second matrix.

• Now, it can be proven that by

      3x2  and 2x3

Therefore, the value of B is 2x3.

And AB order is 3x3

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