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Transpose of Matrix

The matrix obtained from any given matrix A, by interchanging rows and columns, is called the transpose of A and is denoted by AT.
If A = [aij]m × n and AT = [bij]n × m then bij = aji, i, j.
For example, if A = 63287.png, then AT = 63281.png.

Properties of transpose

  • (AT)T = A
  • (A + B)T = AT + BT, A and B being conformable matrices
  • (αA)T = αAT, α being scalar
  • (AB)T = BTAT, A and B being conformable for multiplication (reversal law)

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