Answer and Step-by-step explanation:
Since we have given that
AB = 0
where A and B are n x n matrices.
Consider determinant on both sides,
[tex]\mid AB\mid=\mid 0\mid\\\\\mid A\mid \mid B\mid =0\\\\either\ \mid A\mid =0\ or\ \mid B\mid =0[/tex]
since A is invertible, then |A| ≠ 0
so, it means |B| = 0.
Hence, B is not invertible.
Hence proved.
