A question on matrices properties

[transgalactic]

there is some property of matrices that i forgot
that says that for some kind of matrices there is a given number

that if we will put the given martices to the power of this given number
it will get the zero matrices

for example
0 a
a b

in the power of 3 will change for the first time to
0 0
0 0

what are the laws for this number 3

how do i know the number by looking at the given matrices

 

[morphism]

Such a matrix A is called "http://planetmath.org/encyclopedia/NilpotentMatrix.html ", and the smallest natural number n such that Aⁿ=0 is usually called the "index of nilpotence". Try googling for information -- you'll find a lot.

 

[transgalactic]

i read about them
i understood the transformation
of each step

but i was told the the number comes from the size of the given matrices
which is not true in the case that i showed

the only way that i can find out the number is by practicly
step by step multiplying the matrix by itself.

is there an yeasier way??

 

[morphism]

I'm not familiar with any easier general method.