Matrix Algebra and Determinants (Jee Mains)

Formation, Types & Operations

Medium

Matrix Algebra and Determinants

For some α, β ∈ R, let A = $\left[ {\begin{array}{*{20}{c}} \alpha \\[0.9em] 1 \end{array}\,\,\,\begin{array}{*{20}{c}} 2\\[0.9em] 2 \end{array}} \right]$ and B = $\left[ {\begin{array}{*{20}{c}} 1\\[0.9em] 1 \end{array}\,\,\,\begin{array}{*{20}{c}} 1\\[0.9em] \beta \end{array}} \right]$ be such that A² – 4A + 2I = B² – 3B + I = O.
Then (det(adj(A³ – B³)))² is equal to ………

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