For \(A=\begin{pmatrix}a&b\\c&d\end{pmatrix}\), state adj(A).

Find adj(\(\begin{pmatrix}1&2\\3&4\end{pmatrix}\)).

Use adj(A) to find \(A^{-1}\) for \(A=\begin{pmatrix}1&2\\3&4\end{pmatrix}\).

Find adj(\(\begin{pmatrix}2&-1\\5&3\end{pmatrix}\)).

Verify A adj(A) = \(\det(A)\)I for \(A=\begin{pmatrix}1&2\\3&4\end{pmatrix}\).

For \(A=\begin{pmatrix}3&1\\2&1\end{pmatrix}\), compute \(\det(A)\), adj(A), and \(A^{-1}\).

Explain why the adjugate formula cannot produce an inverse when \(\det(A)\) = 0.

Find all t such that \(A=\begin{pmatrix}t&1\\2&1\end{pmatrix}\) has adj(A) = \(\begin{pmatrix}1&-1\\-2&t\end{pmatrix}\).

For \(A=\begin{pmatrix}0&2\\5&1\end{pmatrix}\), find adj(A) and \(\det(A)\).

A learner says adj(\(\begin{pmatrix}a&b\\c&d\end{pmatrix}\)) = \(\begin{pmatrix}d&c\\b&a\end{pmatrix}\). Diagnose the error.