Define Invertible Matrices. Give an example.

Step 1
An $n\times n$ square matrix A is called Invertible Matrices, if there exists an n x n square matrix B such that AB = BA = I.
$AB=BA=I_n$
$A_{n\times n},B_{n\times n}\text{ and }{I}_n\text{ is identity matrix of }n\times n$
Step 2
In other words, determinant of A is non - zero, then matric A is invertible. $det(A)=|A|\ne 0$
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
$|A|=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$
$=1\cdot (3)-2\cdot (-1)$
$=3+2$
$=5$
$|A|\ne 0\to A\text{ is invertible.}$

Answer is given below (on video)