If, we are given a square matrix A then how to prove that
?
where, k is any scalar, adj(A) is adjoint of matrix A and adj(kA) is adjoint of matrix kA.
Using formula to find inverse of matrices, we can say that
, det(kA) represents determinant of kA matrix.
But, we have {
} and {
}
(1)
We know that
(2)
Putting equation (2) in equation (1), we get
which is the desired result.
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