Properties of Adjoint Matrix. If A, B are square matrices of order n and In is

-1 = n n - T corresponding unit matrix, then (i) A(adjA)=|A|I, = (adj AA (ii) adjA|=|A|*(iii) adj (adjA)=|A|1–2 A;|A|#0 (iv) |adj (adjA)| = | A(n-1)2 (v) adj (AT)=(adj A) (vi) adj(AB)=(adj B)(adj A) (vii) adj (AM)=(adj A)", me N N (viii) adj(kA)= kn-1 (adj A), ke R (ix) adj(In). = In (x) adj (O)=0 т -

(xi) A is symmetric matrix = adj(A) is also symmetric matrix.

(xii) A is diagonal matrix adj (A) is also diagonal matrix xiii) A is triangular matrix = adj (A) is also triangular matrix.

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