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What is the product of a matrix with its own adjoint?

  • A.the identity matrix alone
  • B.the zero matrix in every case
  • C.the transpose of the original matrix
  • D.the determinant times the identity matrix

Answer: D

The relation holds whether or not the matrix is invertible, and dividing through by the determinant is exactly how the inverse formula arises. For a singular matrix it shows the product with the adjoint is the zero matrix.

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