Submatrix of a Matrix

DEFINITION 1.3.4   A matrix obtained by deleting some of the rows and/or columns of a matrix is said to be a submatrix of the given matrix.

For example, if $A=\begin{bmatrix}1 & 4 & 5 \\ 0 & 1 & 2 \end{bmatrix},$ a few submatrices of $A$ are

$$[ 1 ], [ 2 ], \begin{bmatrix}1 \\ 0 \end{bmatrix}, [ 1 \; 5 ], \begin{bmatrix}1 & 5 \\ 0 & 2 \end{bmatrix}, \; A.$$

But the matrices $\begin{bmatrix}1& 4\\ 1& 0 \end{bmatrix}$ and $\begin{bmatrix}1& 4\\ 0& 2 \end{bmatrix}$ are not submatrices of $A.$ (The reader is advised to give reasons.)