This is Nilpotent Matrix
All the eigenvalues of Nilpotent matrix are all 0
Let the eigenvalues of A(n X n matrix) be $\lambda _1, \lambda _2, \lambda _3, .........................\lambda _n$
$\lambda _1 = 0$
$\lambda _1 = 0$
$\lambda _2 = 0$
$\lambda _3 = 0$
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$\lambda _n = 0$
eigenvalues of $A - 3.I \ be \ \lambda _1 -3, \lambda _2-3, \lambda _3-3, .........................\lambda _n-3$ $\because eigenvalues \ of \ A - k.I \ is \ \lambda -k, \ k \ is \ scalar$
eigenvalues of $A - 3.I \ be \ -3, -3, -3, .........................-3$
$determinant \ of \ matrix = product \ of \ eigenvalues$
$(-3) * (-3) * (-3) * (-3) ...................*(-3)$
$(-1)^n.3^n$