If, we have invertible square matrix A, then how to prove that
?
adj(A) is adjoint of A and T represents transpose of matrix.
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How to prove that adjoint(AB)= adjoint(B).adjoint(A) if its given that A and B are two square and invertible matrices.
Using formula to calculate inverse of matrix, we can say that
(1)
adj(AB) is adjoint of (AB) and det(AB) is determinant of (AB).
(2)
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Note: This property holds for square matrices.
If, we are given matrix A then
How to prove that
? where adj(A) is adjoint of A and det(A) is determinant of A.
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Note: This property holds for square matrices which are invertible.
This property of adjoint of matrices can be easily proved using property
where adj(A) is adjoint of A, det(A) is determinant of A and
is inverse of A. A here is an invertible matrix.