# Thread:

1. ## does this mean a matrix is singular?

If a matrix A $\neq$ 0 and $A^k=0$ where k is a positive integer, does that mean A is singular?

2. A must be singular. Suppose not, then there exists $A^{-1}$ satisfying $AA^{-1}=A^{-1}A = I$. Then $A^k (A^{-1})^k = I = 0$, giving a contradiction.

3. so the =0 means a matrix full of zeros right?

4. Originally Posted by superdude
so the =0 means a matrix full of zeros right?
Yes, that is the 0 matrix.
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