Determinant of any square matrix is equal to determinant of its transpose. Lets take an example of any square matrix and find value of its determinant. Then transpose this matrix and again find value of determinant of transpose of matrix. We will note that determinant of matrix is equal to determinant of its transpose.
We have matrix A, how to prove that transpose of (A transpose) is equal to matrix A i.e {A^T)^T = A.
We are given matrix A then how can we prove that
. where T represents transpose of Matrix.
Two matrices are said to be equal if they have same order and their corresponding elements are equal. Similarly, to prove
. we will have to prove that both the sides have same order and both the sides have equal corresponding elements.
We are given a matrix A and scalar k, how to prove that (kA)^T = k(A^T)?
We are given a matrix A and scalar k, we want to prove that
, where T represents transpose of matrix.
Two matrices are said to be equal if they have same order and their corresponding elements are equal. Similarly, if we can prove that both the sides of equation
have same order and their corresponding elements are equal then it means equation
is true.
We have two matrices A and B, how to prove that (A+B)^T is equal to A^T + B^T?
How can we prove that
where A and B are two matrices of same order and T represents transpose of matrix.
Two matrices are equal if they are of same order and their corresponding elements are equal. In the same way, if we can prove that both sides of the equation
have same order and their corresponding elements are equal then it means that the given equation is true.
We are given an invertible matrix A then how to prove that (A^T)^ – 1 = (A^ – 1)^T?
How to prove that
where A is an invertible square matrix, T represents transpose and
In other words we want to prove that inverse of
is equal to
.