How to prove that $$adj(adjA) = {(\det A)^{n - 2}}.A$$ (if A is any invertible matrix) with n>2 We know that $${A^ - } = adj(A)/\det (A)$$ … [Continue reading]
How to prove that det(adj(A))= (det(A)) power n-1?
Note: This property holds for square matrices which are invertible. This property of adjoint of matrices can be easily proved using property $${A^{ - 1}} = {{adj(A)} \over {\det (A)}}$$ where adj(A) is adjoint of A, det(A) … [Continue reading]
What are singular and non-singular matrices?
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 … [Continue reading]
Value of Determinant remains unchanged if we add equal multiples of all the elements of row (column) to corresponding elements of another row (column)
If, we have a given matrix A. We can perform some column and row operations on this matrix such that value of its determinant remains unchanged. If, we multiply particular row (column) of matrix A with a constant k and then add all the element of … [Continue reading]
Determinant of Matrix becomes k times by multiplying any row or column by k
If, we have any given matrix A and we multiply any row or column of matrix with constant k then determinant of modified matrix becomes k times of determinant of A. We can show this by taking example of 3 x 3 matrix A and calculating its determinant. … [Continue reading]
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