Characteristic polynomial The characteristic polynomial of a square matrix \$A\$ is defined as the polynomial \$p_A(x) = \det(Ix-A)\$ where \$I\$ is the identity matrix and \$\det\$ the determinant. Note that this definition always gives us a monic polynomial such that the solution is unique.
Your task for this challenge is to compute the coefficients of the characteristic polynomial for an integer valued matrix, for this you may use built-ins but it is discouraged.
Rules

input is an \$N\times N\$ (\$N \ge 1\$) integer matrix in any convenient format
your program/function will output/return the coefficients in either increasing or decreasing order (please specify which)
the coefficients are normed such that the coefficient of \$x^N\$ is 1 (see test cases)
you don't need to handle invalid inputs

Testcases
Coefficients are given in decreasing order (ie. \$x^N, x^{N-1}, ..., x^2, x, 1\$):
[0] -&gt; [1 0]
[1] -&gt; [1 -1]
[1 1; 0 1] -&gt; [1 -2 1]
[80 80; 57 71] -&gt; [1 -151 1120] 
[1 2 0; 2 -3 5; 0 1 1] -&gt; [1 1 -14 12]
[4 2 1 3; 4 -3 9 0; -1 1 0 3; 20 -4 5 20] -&gt; [1 -21 -83 559 -1987]
[0 5 0 12 -3 -6; 6 3 7 16 4 2; 4 0 5 1 13 -2; 12 10 12 -2 1 -6; 16 13 12 -4 7 10; 6 17 0 3 3 -1] -&gt; [1 -12 -484 3249 -7065 -836601 -44200]
[1 0 0 1 0 0 0; 1 1 0 0 1 0 1; 1 1 0 1 1 0 0; 1 1 0 1 1 0 0; 1 1 0 1 1 1 1; 1 1 1 0 1 1 1; 0 1 0 0 0 0 1] -&gt; [1 -6 10 -6 3 -2 0 0]
SageMath, 3 bytes

5 bytes saved thanks to @Mego

fcp


Try it online!

Takes a Matrix as input.

fcp stands for factorization of the characteristic polynomial,

which is shorter than the normal builtin charpoly.