Question

Exercise 2.1.47 Prove that ifA^-1 exists and AX=0 then X =0.

Answer 1

Explanation:

If
`A^(-1)` exist, then we have that
`A^(-1)\cdot A=1`.

Therefore, in the case that
`AX=0`, if we multiply both

terms in the equation by
`A^(-1)`, then we have

`A \cdot A^(-1)X=A^(-1)0`

and so the equation tells us that

`X=A\cdot A^(-1)X=A^(-1)0=0`.