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# Basic matrix manipulation

The emphasis of the second part of this chapter is on mastering the following operations:

• Scalar multiplication, matrix addition, and matrix multiplication
• Traces and determinants
• Transposes and inverses
• Norms and condition numbers

## Scalar multiplication, matrix addition, and matrix multiplication

Let us start with the matrices stored with the `ndarray` class. We accomplish scalar multiplication with the `*` operator, and the matrix addition with the `+` operator. But for matrix multiplication we will need the instance method `dot()` or the `numpy.dot` function, since the operator `*` is reserved for element-wise multiplication:

```In [54]: 2*A
Out[54]:
array([[ 2,  4],
[ 8, 32]])
In [55]: A + 2*A
Out[55]:
array([[ 3,  6],
[12, 48]])
In [56]: ...```

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