First slide

Applications of determinant

Question

$If A is a square matrix such that A . (a d j A) = [\begin{array}{ccc} 4 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 4 \end{array}] then 3 | adj A | =$

Moderate

A

12
B

48
C

20
D

36

Solution

$A (a d J A) = | A | I = 4 I (g i v e n) \Leftarrow | A | = 4 ∴ 3 | a d j A | = 3 | A |^{3 - 1} = 48$

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