Question

Sejam as matrizes A = [(3,2),(5,7)] e B = [(4,1),(2,3)]. Quanto vale o det(A.B)?

Answer 1

$A \: . \: B \\ \\ \\ \left[\begin{array}{ccc}3&2\\5&7\end{array}\right] \: . \: \left[\begin{array}{ccc}4&1\\2&3\end{array}\right] = \left[\begin{array}{ccc}16&9\\34&26\end{array}\right]_2 \\ \\ \\ det\: (A.B) = \left|\begin{array}{ccc}16&9\\34&26\end{array}\right| = 416 - 306 = 110$

Answer 2

A=
3   2
5,  7     det =21-10 =11

B=
4    1
2    3   det=12-2 =10

det(A*B)  =   det (A) * det(B)  =11*10=110