Question

Is the inverse of a matrix also invertible?

Answer 1

Only if its determinant is non-zero

Explanation:

`A^(-1)` exists `iff det(A)!=0`

Answer 2

Yes.

Explanation:

If a matrix `A` has an inverse `A^(-1)` then it satisfies:

`A A^(-1) = A^(-1)A = I`

Looking at this a different way, the matrix `A` satisfies the definition of an inverse for `A^(-1)`, so `A^(-1)` is also invertible (with inverse `A`).