Realuzar speraciones \( A=\left[\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right] B=\left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \) \( A^{2}-B^{2} \)

Para realizar la operación \( A^{2}-B^{2} \), primero necesitamos calcular los cuadrados de las matrices \( A \) y \( B \), y luego restarlos. Dado que \( A=\left[\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right] \) y \( B=\left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \), podemos calcular los cuadrados de estas matrices de la siguiente manera: \( A^{2} = AA = \left[\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right] \left[\begin{array}{cc}2 & 1 \\ 3 & -3\end{array}\right] \) \( B^{2} = BB = \left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \) Luego, restamos \( B^{2} \) de \( A^{2} \) para obtener el resultado final. Vamos a calcular los cuadrados de las matrices \( A \) y \( B \) y luego restarlos. Matrices by following steps: - step0: Solution: \(\left[\begin{array}{ll}{2}&{1}\\{3}&{-3}\end{array}\right]\times \left[\begin{array}{ll}{2}&{1}\\{3}&{-3}\end{array}\right]\) - step1: Multiply the terms: \(\left[\begin{array}{ll}{2\times 2+1\times 3}&{2\times 1+1\times \left(-3\right)}\\{3\times 2-3\times 3}&{3\times 1-3\left(-3\right)}\end{array}\right]\) - step2: Evaluate: \(\left[\begin{array}{ll}{7}&{-1}\\{-3}&{12}\end{array}\right]\) Calculate or simplify the expression \( \left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \left[\begin{array}{cc}-6 & 5 \\ 2 & -3\end{array}\right] \). Matrices by following steps: - step0: Solution: \(\left[\begin{array}{ll}{-6}&{5}\\{2}&{-3}\end{array}\right]\times \left[\begin{array}{ll}{-6}&{5}\\{2}&{-3}\end{array}\right]\) - step1: Multiply the terms: \(\left[\begin{array}{ll}{-6\left(-6\right)+5\times 2}&{-6\times 5+5\left(-3\right)}\\{2\left(-6\right)-3\times 2}&{2\times 5-3\left(-3\right)}\end{array}\right]\) - step2: Evaluate: \(\left[\begin{array}{ll}{46}&{-45}\\{-18}&{19}\end{array}\right]\) Calculate or simplify the expression \( \left[\begin{array}{ll}{7}&{-1}\\{-3}&{12}\end{array}\right]-\left[\begin{array}{ll}{46}&{-45}\\{-18}&{19}\end{array}\right] \). Matrices by following steps: - step0: Solution: \(\left[\begin{array}{ll}{7}&{-1}\\{-3}&{12}\end{array}\right]-\left[\begin{array}{ll}{46}&{-45}\\{-18}&{19}\end{array}\right]\) - step1: Rewrite the expression: \(\left[\begin{array}{ll}{7}&{-1}\\{-3}&{12}\end{array}\right]+\left[\begin{array}{ll}{-46}&{45}\\{18}&{-19}\end{array}\right]\) - step2: Evaluate: \(\left[\begin{array}{ll}{7-46}&{-1+45}\\{-3+18}&{12-19}\end{array}\right]\) - step3: Evaluate: \(\left[\begin{array}{ll}{-39}&{44}\\{15}&{-7}\end{array}\right]\) El resultado de \( A^{2}-B^{2} \) es: \( A^{2}-B^{2} = \left[\begin{array}{ll}{-39}&{44}\\\\{15}&{-7}\end{array}\right] \)