If A and B are non-singular matrices of order 3 × 3 , such that A = adj B and B = adj A , then det A + det B is equal to (where det ( M ) represents the determinant of matrix M and adj M represents the adjoint matrix of matrix M )

Question

If A and B are non-singular matrices of order 3 × 3 , such that A = adj B and B = adj A , then det A + det B is equal to (where det ( M ) represents the determinant of matrix M and adj M represents the adjoint matrix of matrix M ), 1, 2, 3, 4

MARKS App · Accepted Answer

A = adj B = adj adj A = A A ⇒ A = A 4 ⇒ A = 1 ⇒ B = 1 Hence, A + B = 2

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