Let A and B be two 3 $\times$ 3 matrices such that $AB = I$ and $|A| = {1 \over 8}$. Then $|adj\,(B\,adj(2A))|$ is equal to
Solution
<p>A and B are two matrices of order 3 $\times$ 3.</p>
<p>and $AB = I$,</p>
<p>$|A| = {1 \over 8}$</p>
<p>Now, $|A||B| = 1$</p>
<p>$|B| = 8$</p>
<p>$\therefore$ $|adj(B(adj(2A))| = |B(adj(2A)){|^2}$</p>
<p>$= |B{|^2}|adj(2A){|^2}$</p>
<p>$= {2^6}|2A{|^{2 \times 2}}$</p>
<p>$= {2^6}.\,{2^{12}}.\,{1 \over {{2^{12}}}} = 64$</p>
About this question
Subject: Mathematics · Chapter: Matrices and Determinants · Topic: Types of Matrices and Operations
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