Let A be a matrix of order 3 [] 3 and det (A) = 2.

Question

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 \_\_\_\_\_\_\_\_\_\_\_\_\_.

Accepted Answer

$|A| = 2$

$$||A| = adj\,(5\,adj\,{A^3})|$$

$$ = |25|A|adj\,(adj\,{A^3})|$$

$$ = {25^3}|A{|^3}\,.\,|adj\,{A^3}{|^2}$$

$$ = {25^3}\,.\,{2^3}\,.\,|{A^3}{|^4}$$

$$ = {25^3}\,.\,{2^3}\,.\,{2^{12}} = {10^6}\,.\,512$$

Solutions · 1