Matrix Determinant and Adjoint Properties (Jee …

Determinants

Medium

Matrix Determinant and Adjoint Properties

Let a ∈ R and A be a matrix of order 3 × 3 such that det(A) = –4 and $A + I = \left[ {\begin{array}{*{20}{c}} 1&a&1\\[0.9em] 2&1&0\\[0.9em] a&1&2 \end{array}} \right]$ , where I is the identity matrix of order 3 × 3.
If det ((a + 1)adj((a–1)A)) is 2^m3ⁿ, m, n ∈ {0,1,2,…..20}, then m + n is equal to :

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