Adjoint Matrix Invertibility

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If matrix A is invertible, is its adjoint matrix also always invertible?

The book "Elementary Linear Algebra" by Anton and Rorres use the terms adjucate matrix, adjoint matrix, and classical adjoint matrix interchangeably. Is there a difference between them? From my limited experience, I think there is. In this problem I am referring to the adjoint matrix as the transpose of the cofactor matrix from A.

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1 Answer

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By Cramer's rule, the adjoint of an invertible matrix equals its inverse times its determinant. Now, is that invertible?

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