Lecture on Inverse of Matrix
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Adjoint and inverse of Matrix:
$A^-1=adj(A)/|A|$
where, |A| ≠ 0.
A is a non-singular and square matrix.
$adj(A)=[cofactor(A)]^t$

Ques. If $A= \begin{bmatrix}a&b\\c&d\end{bmatrix}$   , cofactor(A) ?

$cofactor(A)= \begin{bmatrix}d&-c\\-b&a\end{bmatrix}^t= \begin{bmatrix}d&-b\\-c&a\end{bmatrix}$
$A^-1=adj(A)/|A|=1/(ad-bc) \begin{bmatrix}d&-b\\-c&a\end{bmatrix}$

Properties of inverse:

1. $AA^-1=I=A^-1A$
2. $(AB)^-1=B^-1A^-1$
3. $(A')^-1=(A^-1)'$
4. $(A^-1)\theta=(A\theta)^-1$
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