Write the \(3\times 3\) identity matrix.

Write the \(2\times 4\) zero matrix.

For \(A=\begin{pmatrix}2&-1\\3&4\end{pmatrix}\), compute AI_2.

For \(A=\begin{pmatrix}2&-1\\3&4\end{pmatrix}\), compute 0A where 0 is the \(2\times 2\) zero matrix.

If A is \(3\times 5\), which identity matrix makes AI valid: \(I_3\), \(I_5\), or both?

If A is \(3\times 5\), which identity matrix makes IA valid: \(I_3\), \(I_5\), or both?

Compute \(\begin{pmatrix}1&2&3\\4&5&6\end{pmatrix}\)\(I_3\).

Find x and y if \(\begin{pmatrix}x&0\\0&y\end{pmatrix}\) is the \(2\times 2\) identity matrix.

For \(A=\begin{pmatrix}1&-2\\0&3\end{pmatrix}\) and \(B=\begin{pmatrix}4&5\\-1&2\end{pmatrix}\), simplify \(A0\) + BI_2, where 0 is the \(2\times 2\) zero matrix.

A student says the zero matrix and identity matrix are the same because both are special square matrices. Diagnose the error using \(2\times 2\) examples.