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If the order of matrix A is 2×3 and order of matrix B is 3×4 then A and B are said

to be compatible for multiplication and the order of the product matrix A×B will be

2 ×4. In general, if A is a matrix of order m×p and B is a matrix of order p×n, then the

product matrix A×B will be of order m×n.

Knowledge of all the basic ideas in matrices, may enable the child to understand the

concept of matrix multiplication also when it is taught with examples.

Eg. : Let, A = ⎟⎟
⎠

⎞

⎜⎜⎝

= ⎛

⎟⎟⎠

⎞

⎜⎜⎝

⎛

− - 2 3 1

B 4 2 0

2 1

1 3

Here the order of matrix A is 2×2 and the order of the matrix B is 2×3. That is the

number of columns of the first matrix is equal to the number of rows of the second

matrix. Hence the product of A and B is possible.

In finding the product of any two matrices, the elements of the first row of the first

matrix are multiplied and added with the elements of the first column of the second

matrix. Then the elements of first row of first matrix are multiplied and added with

elements of second column of the second matrix and so on.

Therefore, the product of A and B, that is

AB = ⎟⎟⎠

⎞

⎜⎜⎝

⎛

⎟⎟⎠

⎞

⎜⎜⎝

⎛

− - 2 3 1

4 2 0

2 1

1 3

1 2

3

(^456)

= ⎟⎟

⎠

⎞

⎜⎜⎝

⎛

× + − × − × + − × × + − ×

× + ×− × + × × + ×

2 4 ( 1 ) ( 2 ) 2 2 ( 1 ) 3 2 0 ( 1 ) ( 1 )

( 1 4 ) ( 3 2 ) 1 2 3 3 1 0 3 1

= ⎟⎟⎠

⎞

⎜⎜⎝

⎛

+ − −

− + +

8 2 4 3 0 1

4 6 2 9 0 3

= ⎟⎟

⎠

⎞

⎜⎜⎝

⎛

−

−

10 1 1

2 11 3