Scalars are just single numbers. They are written in italics.
A vector is an array of numbers. Each number has an index.
A matrix is a 2-D array of numbers, so each element has 2 indices instead of one.
With Matrices, we have the concept of a Transpose. A transpose of a matrix is the mirror image of the matrix along a diagonal line (main diagonal).
3x2 Matrix
The resulting matrix will be 2x3
These are arrays with more than two axes. This is an array of numbers arranged on a gird with variable number of axes. This means an element could have coordinates such as $Ai,j,k$.
For C = AB to be possible where A,B are two matrices and C is the resulting matrix.