Identity matrix “ construct “ I'm not sure if the tags I added are the right ones ... correct me if I'm wrong
name of course I study is Computer Programming. 
I have solved all the homework problems. This is the last question I didn't understand.
Construct the matrix 
$$B=\pmatrix{     1   &     2   &      3\\
                  4     &  2    &    6\\ 
                          -3  &    -1  &     -3\\
}$$
Show that $B \times B \times B$ is a scalar multiple of the identity matrix and find the scalar.
I don't need you to give me an answer, help me understand how to solve it.
Thanks 
Edit:
I am sorry I think I didn't make it clear ..  I am solving the homework on R program.. how to write the answer?  How can I enter the matrix on the program so I can multiply it ? 
 A: You just have to multiply B by itself 3 times. You will find the result to be a diagonal Matrix equal to a scalar multiplied by the identity matrix. 
So basically you need to find a scalar $a \in \mathbb{R}$ which satisfies 
$B(BB) = \begin{pmatrix}a&0&0\\0&a&0\\0&0&a\\ \end{pmatrix} $
A: $$B = \begin{pmatrix} 1&2&3\\4&2&6\\-3&-1&-3\end{pmatrix}$$
$$B\times B = \begin{pmatrix} 0&3&6\\-6&6&6\\2&-5&-6\end{pmatrix}$$
$$B\times B \times B = \begin{pmatrix} -6&0&0\\0&-6&0\\0&0&-6\end{pmatrix}= -6 I$$
A: $$B^2=B \times B=\pmatrix{     1   &     2   &      3\\
                  4     &  2    &    6\\ 
                          -3  &    -1  &     -3\\
}\pmatrix{     1   &     2   &      3\\
                  4     &  2    &    6\\ 
                          -3  &    -1  &     -3\\
}=\pmatrix{     0  &     3   &      6\\
                  -6     &  6    &    6\\ 
                          2  &    -5  &     -6\\
}$$
$$B \times B^2=\pmatrix{     1   &     2   &      3\\
                  4     &  2    &    6\\ 
                          -3  &    -1  &     -3\\
}\pmatrix{     0  &     3   &      6\\
                  -6     &  6    &    6\\ 
                          2  &    -5  &     -6\\
}=\pmatrix{     -6  &     0   &      0\\
                       0&  -6    &    0\\ 
                          0  &    0 &     -6\\}=-6 \times I_3$$
