What is the meaning of an invertible matrix?
Understand the Problem
The question is asking for the definition or explanation of an invertible matrix, which is a type of matrix that has an inverse. This means that when the matrix is multiplied by its inverse, the result is the identity matrix. This inquiry may involve some concepts related to linear algebra.
Answer
An invertible matrix has an inverse that, when multiplied by the original matrix, results in the identity matrix.
The final answer is an n x n matrix A is invertible if there exists another n x n matrix B such that AB = BA = I, where I is the identity matrix.
Answer for screen readers
The final answer is an n x n matrix A is invertible if there exists another n x n matrix B such that AB = BA = I, where I is the identity matrix.
More Information
An invertible matrix, also known as a non-singular or non-degenerate matrix, implies that the matrix has a determinant that is not zero.
Tips
One common mistake is assuming all square matrices are invertible. Only those with a non-zero determinant are invertible.
Sources
- Invertible matrix - Wikipedia - en.wikipedia.org
- Invertible matrix | Definition, Properties, & Facts - Britannica - britannica.com
- The web page with info on - BYJU's - byjus.com
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