Mar 3, 2026 · If $A$ and $B$ are $n \times n$ invertible matrices then prove that $AB$ is invertible Ask Question Asked 16 days ago Modified 15 days ago

17 Gauss-Jordan elimination can be used to determine when a matrix is invertible and can be done in polynomial (in fact, cubic) time. The same method (when you apply the opposite row operation to …

Aug 30, 2021 · And a function is invertible if and only if it is one-to-one and onto, i.e. the function is a bijection. This is not necessarily a definition of invertible, but it a useful and quick way of deciding if a …

4 I always got taught that if the determinant of a matrix is $0$ then the matrix isn't invertible, but why is that? My flawed attempt at understanding things: This approaches the subject from a geometric point …

1 we want to proove that A is invertible if the column vectors of A are linearly independent. we know that if A is invertible than rref of A is an identity matrix so the row vectors of A are linearly independent.

How can we show that $ (I-A)$ is invertible? Ask Question Asked 14 years, 1 month ago Modified 7 years, 3 months ago

Aug 3, 2018 · The question was why an invertible matrix can be row reduced to the identity matrix, not why row operations can be described by matrices.

Nov 15, 2017 · From my understanding, invertible means non-singular and any of eigenvalue must not be 0. Exactly. In fact, a matrix is singular if and only if $0$ is its eigenvalue. Diagonalizable means …

Jul 10, 2017 · In doing so, clearly the set of vectors can be thought of as column vectors of A. So saying "the vectors for A" is a completely natural thing to say, and should be unambiguous. here is an …

Sep 3, 2017 · A function is invertible if and only if it is injective (one-to-one, or "passes the horizontal line test" in the parlance of precalculus classes). A bijective function is both injective and surjective, thus …