Explanation:

The transpose of a rectangular matrix is a matrix obtained by interchanging its rows with columns. Let's consider a rectangular matrix A with dimensions m x n.

Definition of Transpose:
The transpose of matrix A is denoted by Aᵀ and is obtained by interchanging its rows with columns. If A has dimensions m x n, then Aᵀ will have dimensions n x m.

Example:
Let's consider a rectangular matrix A with dimensions 2 x 3:

A = [1 2 3
4 5 6]

To find the transpose of A, we interchange its rows with columns:

Aᵀ = [1 4
2 5
3 6]

Explanation of Options:
a) Rectangular Matrix: A rectangular matrix is a matrix that has different numbers of rows and columns. The transpose of a rectangular matrix will also have different numbers of rows and columns, making it a rectangular matrix. Therefore, option 'A' is correct.
b) Diagonal Matrix: A diagonal matrix is a square matrix in which all the elements outside the main diagonal are zero. The transpose of a rectangular matrix will not necessarily result in a diagonal matrix.
c) Square Matrix: A square matrix is a matrix that has an equal number of rows and columns. The transpose of a rectangular matrix will not result in a square matrix unless it is initially a square matrix.
d) Scalar Matrix: A scalar matrix is a square matrix in which all the diagonal elements are equal and all the non-diagonal elements are zero. The transpose of a rectangular matrix will not necessarily result in a scalar matrix.

Therefore, the correct answer is option 'A', a rectangular matrix.