Kyran Hudson

2020-12-28

Define Invertible Matrices. Give an example.

Nathalie Redfern

Step 1
An $n×n$ square matrix A is called Invertible Matrices, if there exists an n x n square matrix B such that AB = BA = I.
$AB=BA={I}_{n}$

Step 2
In other words, determinant of A is non - zero, then matric A is invertible. $det\left(A\right)=|A|\ne 0$
Step 3
For example, let us assume
$A=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$
Step 4
So, the determinant of A is
$|A|=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$
$=1\cdot \left(3\right)-2\cdot \left(-1\right)$
$=3+2$
$=5$

Jeffrey Jordon