Can we multiply a matrix by an imaginary or complex number not purely real? I am currently reading the topic of scalar multiplication of matrices. It always says that if k is a scalar then k times matrix = matrix with all the elements multiplied by k.
My question is what is this scalar. Like we know complex numbers are very similar to the vectors.
so is it only the purely real ks we are talking about or we can multiply a matrix by 2+3i also for example.

The short answer is yes, you can multiply a real matrix by a complex scalar. You can even multiply it by a vector whose components are complex numbers. But this simple answer gives little explanation.
The thorough answer is that when we do linear algebra, we really need to specify over which field we are constructing our matrices (and vectors). This is important because it affects the question of the dimension of the relevant vector space. So to answer your question, in which space the possible scalars (and entries) reside must be declared when defining the relevant vector space. If you are working with $\mathbb{R}^{m \times n}$, i.e. the set of all $m \times n$ matrices with real entries, viewed as a real vector space, it is understand that the scalars reside in $\mathbb{R}$. However, you could also work with $\mathbb{R}^{m \times n}$ viewed as a subspace of $\mathbb{C}^{m \times n}$, in which case it would be natural to allow multiplication by complex scalars.
