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Answer 1

$\huge\red{\underline{\overline{\mathbb{√\ηsωεя:-}}}}$ ━━━━━━━━━━━━━━━━━━━━━━━━━━━━

multiplicative inverse of a matrix is similar in concept, except that the product of matrix \displaystyle AA and its inverse \displaystyle {A}^{-1}A−1

equals the identity matrix. The identity matrix is a square matrix containing ones down the main diagonal and zeros everywhere else. We identify identity matrices by \displaystyle {I}_{n}I

n

where $\displaystyle nn represents the dimension of the matrix. The equations below are the identity matrices for a \displaystyle 2\text{}\times \text{}22×2 matrix and a \displaystyle 3\text{}\times \text{}33×3 matrix,$ respectively.

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The identity matrix acts as a 1 in matrix algebra. For example, \displaystyle AI=IA=AAI=IA=A.

A matrix that has a multiplicative inverse has the properties

\displaystyle \begin{array}{l}A{A}^{-1}=I\\ {A}^{-1}A=I\end{array}

AA−1 =IA−1 A=I

A matrix that has a multiplicative inverse is called an invertible matrix. Only a square matrix may have a multiplicative inverse, as the reversibility, \displaystyle A{A}^{-1}={A}^{-1}A=IAA

−1=A−1

A=I, is a requirement. Not all square matrices have an inverse, but if \displaystyle AA is invertible, then \displaystyle {A}^{-1}A−1

is unique. We will look at two methods for finding the inverse of a$\displaystyle 2\text{}\times \text{}22×2 matrix and a third method that can be used on both \displaystyle 2\text{}\times \text{}22×2 and \displaystyle 3\text{}\times \text{}33×3 matrices.$

$\huge\blue{Hope\: it\: helps}$

Answer 2

May ItS Help✌✌✌✌

Look at attached ❤