Question

Let A and B be nxn matrices such that AB is singular prove that either A or Bis singular

Answer 1

`\det(\mathbf{AB})=\det\mathbf A*\det\mathbf B`

Because
`\mathbf{AB}` is singular, we have


`\det(\mathbf{AB})=0`

from which it follows that either
`\det\mathbf A=0` or
`\det\mathbf B=0`.