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Idempotent Matrix

A square matrix A is called an idempotent matrix if A2 = A.


Properties of transpose of a matrix

527.png 

  • (A + B)T = AT + BT
  • (pA)T = pAT
  • (AB)T = BTAT (not ATBT)
  • AAT = ATA

Inverse of a Matrix

A–1 = 552.png

Properties of Inverse of Matrix

  • (A–1)–1 = A
  • (AB)–1 = B–1A–1
  • (KA)–1 = K–1A–1 = 572.png
  • | A–1 | = 582.png
  • adj. (AB) = (adj. B) (adj. A)
  • | adj. A| = | A |n–1 where A is square matrix.





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