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In this chapter, we will discuss the Multiplication and Dot Product of two NumPy arrays.

**Multiplication**

Multiplication between two NumPy arrays is an element-wise product, and is represented by '`*`

'

e.g.

```
import numpy as np
A = np.array( [ [ 1,1], [0, 1] ] )
B = np.array( [ [2, 0], [3, 4] ] )
```

Please note, this element-wise product '`*`

' is different from 'dot product '`.`

' of matrices.

'dot product' is also known as 'matrix product'.

```
M = A * B
print(A)
array([ [1, 1],
[0, 1] ])
print(B)
array( [ [2, 0],
[3, 4] ] )
print(M)
```

Output (M) will be

```
array([ [2, 0 ],
[0, 4] ] )
```

Above, element-wise product(M) is computed as below

```
M = [ [ A[1, 1] * B[1, 1], A[1, 2] * B[1, 2] ],
[ A[2, 1] * B[2, 1], A[2, 2] * B[2, 2] ] ]
= [ [ (1 * 2), (1 * 0)],
[ (0 * 3), (1, 4) ] ]
M = [ [2, 0],
[0, 4] ]
```

**Matrix Product (or Dot Product)**

Matrix Product (or Dot Product) between two NumPy is different from the element-wise product (or Multiplication). The dot product is represented by '`.`

'

e.g.

```
import numpy as np
C = np.array( [ [ 1,1], [0, 1] ] )
D = np.array( [ [2, 0], [3, 4] ] )
```

Please note, this dot product '`.`

' or 'matrix product' is different from 'element-wise' product '`*`

'

```
P = np.dot(C, D)
print(C)
array([ [1, 1],
[0, 1] ])
print(D)
array( [ [2, 0],
[3, 4] ] )
print(P)
```

Output (P) will be

```
array([ [5, 4 ],
[ 3, 4] ] )
```

Above, element-wise product(P) is computed as below

```
P = [ [ [( (C[1,1] * D[1, 1]) + (C[1, 2] * D[2, 1] ) )], [( (C[1,1] * D[1, 2]) + (C[1, 2] * D[2, 2] ) )] ],
[ [( (C[2,1] * D[1, 1]) + (C[2, 2] * D[2, 1] ) )], [( (C[2,1] * D[1, 2]) + (C[2, 2] * D[2, 2] ) )] ] ]
= [ [ ( (1 * 2) + (1 * 3) ), ( (1 * 0) + (1 * 4) ) ],
[ ( (0 * 2) + (1 * 3) ), ( (0 * 2) + (1 * 4) ) ] ]
= [ [ (2 + 3), (0 + 4) ],
[ (0 + 3), (0 + 4) ] ]
= [ [5, 4],
[3, 4] ]
```

Please follow the below steps:

(1) Please import required libraries

```
import numpy as np
```

**Multiplication (element-wise product)**

(2) Create two NumPy arrays - `A_arr`

and `B_arr`

- as shown below

```
A_arr = np.array([ [ 5,9], [4, 7] ])
B_arr = np.array( [ [2, 8], [1, 6] ] )
```

(3) Multiply the above two NumPy arrays (`A_arr`

and `B_arr`

) and store the result in a variable `M_arr`

```
<<your code comes here>> = A_arr << your code comes here>> B_arr
```

(4) Print the array `M_arr`

to see its values

```
print(<<your code comes here>>)
```

**Dot Product (Matrix Product)**

(1) Create two NumPy arrays - `C_arr`

and `D_arr`

- as shown below

```
C_arr = np.array([ [ 5,9], [4, 7] ])
D_arr = np.array( [ [2, 8], [1, 6] ] )
```

(2) Perform dot product of the above two NumPy arrays (`C_arr`

and `D_arr`

) and store the result in a variable `P_arr`

```
<<your code comes here>> = np.dot(<<your code comes here>>)
```

(3) Print the array `P_arr`

to see its values

```
print(<<your code comes here>>)
```

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