1.23 Find the characteristic polynomial of a matrix

$$\left(\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 0\end{array}\right)$$

Mathematica

a = {{1,2,3},{4,5,6},{7,8,0}}; 
CharacteristicPolynomial[a,x]
 

$$-x^3+6x^2+72x+27$$

Matlab

Note: Matlab and Maple generated characteristic polynomial coefficients are negative to what Mathematica generated.

But the sign difference is not important.

clear all; 
A=[1 2 3;4 5 6;7 8 0]; 
 
p=poly(A) 
poly2str(p,'x')
 

p = 
 1.0000 -6.0000 -72.0000 -27.0000 
ans = 
 x^3 - 6 x^2 - 72 x - 27
 

Maple

restart; 
A:=Matrix([[1,2,3],[4,5,6],[7,8,0]]); 
LinearAlgebra:-CharacteristicPolynomial(A,x)
 

$$x^3-6x^2-72x-27$$