We are given matrix A, how can we find its transpose. To find transpose of matrix, it is necessary to understand definition of transpose of matrix.
If
then its transpose which is written as
1. When we find transpose of any matrix then order of matrix gets reversed. For example, if we are given a 2 x 3 matrix, then transpose of this matrix would be a 3 x 2 matrix.
2. Element present at
position in a given matrix A goes to
position in transpose of matrix A.
Lets take an example, we want to find transpose of matrix
Then,
(1) Note that element present at
position in matrix A is at
position in
. For example -2 is present in first row and second column of matrix A which is
position in matrix. Same element is present in first column and second row in
which is
position.
(2) Also, note that order of matrix got reversed. Order of matrix A is 2 x 3 whereas order of
becomes 3 x 2.
(3) First Row (1, -2, 5) present in matrix A becomes first column in
. Second row (6, 1, 4) in matrix A becomes second column in
. Similarly all the columns of matrix A become corresponding rows in
.
[…] that {({A^T})^{ – 1}} = {({A^{ – 1}})^T} where A is an invertible square matrix, T represents transpose and {A^{ – 1}} is inverse of matrix […]