Let A be a matrix of order 3 $\times$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.
Solution
<p>$|A| = 2$</p>
<p>$||A| = adj\,(5\,adj\,{A^3})|$</p>
<p>$= |25|A|adj\,(adj\,{A^3})|$</p>
<p>$= {25^3}|A{|^3}\,.\,|adj\,{A^3}{|^2}$</p>
<p>$= {25^3}\,.\,{2^3}\,.\,|{A^3}{|^4}$</p>
<p>$= {25^3}\,.\,{2^3}\,.\,{2^{12}} = {10^6}\,.\,512$</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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