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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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.
The matrices are said to be singular if their determinant is equal to zero. For example, if we have matrix A whose all elements in the first column are zero. Then, by one of the property of determinants, we can say that its determinant is equal to zero. Hence, A would be called as singular matrix.