Question

Se A = 1 −1 0 2 e B = 1 5 2 0 então det(AB) é:

a) -20

b) -10

c)0

d) 10

e)20

Answer 1

A =  

    1    -1

    0     2  

det(A)=1*2-0*(-1) =2

B =  

    1     5

    2     0

det(B)=1*0-2*5=-10

>> det(A*B)  = det(A)*det(B) =2 * (-10)=  -20

Letra A

Answer 2

$\large\boxed{\begin{array}{l} \rm \: A = \begin{bmatrix} 1& - 1 \\ 0&2\end{bmatrix} \\ \\ \rm \: det( A) = 1 \times 2 - ( - 1) \times 0 \\ \\ \rm \: det( A) = 2 - 0 \\ \\ \rm \: det( A) = 2 \\ \\ \rm \: B = \begin{bmatrix} 1&5 \\ 2&0\end{bmatrix} \\ \\ \rm \: det(B )=1 \times 0 - 5 \times 2 \\ \\ \rm \: det( B) = 0 - 10 \\ \\ \rm \: det(B) = - 10 \\ \\ \rm \: det( A\times B) =2 \times( - 10 )\\ \\ \boxed{ \boxed{ \rm{det(A\times B) = - 20}}} \leftarrow \textsf{Letra A}\end{array}}$