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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