Enunciado
Sean $$A=\begin{bmatrix}a_{11}&a_{12} \\ a_{21}&a_{22}\end{bmatrix},\ B=\begin{bmatrix}b_{11}&b_{12} \\ b_{21}&b_{22}\end{bmatrix}.$$
- Escriba el producto $AB$.
- Calcule $\det A$, $\det B$ y $\det(AB)$.
- Demuestre que $\det(AB)=(\det A)(\det B)$.
Solución Paso a Paso
Verificado
Paso 1 1 de 5
a) Multiplicación de matrices $2\times2$:$$AB=\begin{bmatrix}a_{11}b_{11}+a_{12}b_{21}&\ a_{11}b_{12}+a_{12}b_{22} \\ a_{21}b_{11}+a_{22}b_{21}&\ a_{21}b_{12}+a_{22}b_{22}\end{bmatrix}.$$