Let \( A=\left[\begin{array}{ll}1 & \frac{1}{3} \\ c & d\end{array}\right] \). Find \( c \) and \( d \) such that \( A^{2}=-I_{2} \)

Calcule todos los valores de a para los cuales la matriz \( A=\left[\begin{array}{lll}a & 0 & 4 \\ 1 & 1 & a \\ a & 1 & 2\end{array}\right] \) es no invertit

Rewrite the following without an exponent \[ (-7)^{-2} \]

Simplify. \( [32-(15+5) \div 4]-[56 \div(8-1)]^{\prime} \) \( [32-(15+5) \div 4]-[56 \div(8-1)]=\square \)

\begin{tabular}{l|l}\( \begin{array}{l}\text { Simplify the expression so that no negative exponents } \\ \text { appear in the final result. Assume all variables represent } \\ \text { nonzero real numbers. }\end{array} \) & \( \begin{array}{l}\left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}=\square \\ \\ \left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}\end{array} \) \\ exponents only.) \end{tabular}

\( 1 \leftarrow \) Show that \( A I=I A=A \). \( A=\left[\begin{array}{rr}1 & 8 \\ -2 & 2\end{array}\right] \)