Find the inverse of \(\begin{pmatrix}2&0\\0&5\end{pmatrix}\).

Use the \(2\times 2\) formula to find the inverse of \(\begin{pmatrix}1&2\\3&4\end{pmatrix}\).

Use the \(2\times 2\) formula to decide whether \(\begin{pmatrix}2&6\\1&3\end{pmatrix}\) has an inverse.

Set up the augmented matrix used to find the inverse of \(A=\begin{pmatrix}1&2\\3&4\end{pmatrix}\) by row reduction.

Complete the inverse computation: \(\begin{pmatrix}1&2&1&0\\0&-2&-3&1\end{pmatrix}\) is obtained while reducing [A | I]. Continue to find \(A^{-1}\).

Verify that \(\begin{pmatrix}0&1\\1&0\end{pmatrix}\) is its own inverse.

Find all real t such that \(\begin{pmatrix}t&1\\2&1\end{pmatrix}\) has an inverse.

Use \(A^{-1}\) = \(\begin{pmatrix}1&-2\\0&1\end{pmatrix}\) to solve Ax = \(\begin{pmatrix}3\\5\end{pmatrix}\).

A row reduction of [A | I] produces \(\begin{pmatrix}1&0&2&-1\\0&0&3&4\end{pmatrix}\). Explain why A has no inverse.

A learner tries to find the inverse of a \(2\times 3\) matrix by augmenting it with \(I_2\). Diagnose the error.