Transpose of a matrix :
The matrix which is obtained by interchanging the elements in rows and columns of the given matrix A is called transpose of A and is denoted by A^{T} (read as A transpose).
If order of A is m x n then order of A^{T} is n x m . We note that (A^{T} )^{T} = A.
Question 1 :
If A =
find A^{T}.
Solution :
To find the transpose of the given matrix, we have to write the elements in the rows as columns and the elements in the columns as rows.
Question 2 :
If A =
find -A^{T}.
Solution :
Question 3 :
If A =
then verify (A^{T} )^{T} = A.
Solution :
Hence proved.
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