If A and B are square matrices of the same order, then (AB′ - BA′) is a:
If A and B are square matrices of the same order, then (AB′ - BA′) is a: Correct Answer <span class="fontstyle0">Skew Symmetric matrix.</span>
Concept:
Transpose of a Matrix:
The new matrix obtained by interchanging the rows and columns of the original matrix is called as the transpose of the matrix.
It is denoted by A' or AT.
A symmetric matrix is a square matrix that is equal to its transpose. Formally, A is symmetric if and only if A = A'.
A skew-symmetric matrix is a square matrix that is equal to its transpose. Formally, A is skew-symmetric if and only if A = - A'.
Calculation:
Consider the transpose of the matrix (AB′ - BA′).
(AB′ - BA′)'
= (AB′)' - (BA′)'
= A'B - B'A
= -(AB′ - BA′)
Hence, the matrix is Skew Symmetric.
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Feb 20, 2025