For \(A=\begin{pmatrix}2&-1&0\\5&3&4\end{pmatrix}\), state the size of A.

For \(A=\begin{pmatrix}2&-1&0\\5&3&4\end{pmatrix}\), find the entry a_23.

For \(B=\begin{pmatrix}1&7\\0&-2\\4&5\end{pmatrix}\), write down the second row and the first column.

Decide whether C = \(\begin{pmatrix}3&1\\2&0\end{pmatrix}\) is square. If it is square, state its order.

For D = \(\begin{pmatrix}6\\-1\\8\end{pmatrix}\), state whether D is a row vector, a column vector, or neither, and give its size.

Let A be a \(4\times 5\) matrix. Which entries exist: a_45, a_54, a_11, and a_06?

Construct the \(2\times 3\) matrix A whose entries are given by \(a_ij=i\) + j.

Construct the \(3\times 2\) matrix B whose entries are b_ij = 2i - j.

Find x and y if \(\begin{pmatrix}x&2\\3&y\end{pmatrix}\) = \(\begin{pmatrix}5&2\\3&-1\end{pmatrix}\).

A matrix A has entries \(a_ij=0\) whenever i != j and \(a_ii=1\) for every valid i. If A is \(3\times 3\), write A explicitly.