A matrix raised to a high power ($87$) So, I have this matrix: $$\pmatrix {0&0&0&-1\\1&0&0&0\\0&1&0&0\\0&0&1&0}^{87}$$
My teacher never discussed eigenvalues. So, I do not know what they are and there must be another way to do this (without multiplying the matrix $87$ times). 
Thanks for your help.

It is easy to work with this sparse matrix, because its powers remain sparse.
So 
$$A^2 = \pmatrix{
0&0&-1&0\\
0&0&0&-1\\
1&0&0&0\\
0&1&0&0}
$$
$$A^4 = (A^2)^2 = \pmatrix{
-1&0&0&0\\
0&-1&0&0\\
0&0&-1&0\\
0&0&0&-1} = -I
$$
$$A^8 = (-I)^2 = I$$
So for integer $n$, $A^{8n} = I$.  Then $A^{80} = I$, and $A^{84} = -I$. So
$$A^{86} = -A^2 = \pmatrix{
0&0&1&0\\
0&0&0&1\\
-1&0&0&0\\
0&-1&0&0}
$$
and 
$$A^{87} = -A^3 = \pmatrix{
0&1&0&0\\
0&0&1&0\\
0&0&0&1\\
-1&0&0&0}
$$
