In linear algebra, they talk about a matrix being an inverse and a matrix being invertible. Is there a difference because they seem like the same thing, but when I reading about them, sometimes they seem like there related, but different. So is their a difference? Or can the words inverse and invertible be used interchangeably?
[Math] Inverse vs Invertible
linear algebra
Best Answer
As said in the comments, inverse is a noun and invertible is an adjective. If a matrix is invertible, then it has an inverse. Here's the definition of an inverse:
Definition A matrix $B$ is said to be the inverse of a matrix $A$ if and only if $$AB = BA = I,$$ where $I$ is the identity matrix. In this case, we write $B = A^{-1}$. When the matrix $B = A^{-1}$ exists, we say that $A$ is invertible.
Is this clear enough? I will be happy to clarify anything in the comments.