Kyran Hudson

2020-12-28

Define Invertible Matrices. Give an example.

Nathalie Redfern

Skilled2020-12-29Added 99 answers

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

$|A|=\left[\begin{array}{cc}1& -1\\ 2& 3\end{array}\right]$

$=1\cdot (3)-2\cdot (-1)$

$=3+2$

$=5$

$|A|\ne 0\to A\text{is invertible.}$

An

Step 2

In other words, determinant of A is non - zero, then matric A is invertible.

Step 3

For example, let us assume

Step 4

So, the determinant of A is

Jeffrey Jordon

Expert2022-01-22Added 2575 answers

Answer is given below (on video)