If A = [ 2 1 0 3 1 2 0 4 - 1 ] , then | adj ( A ) | is equal to:

Question

If $A = [\begin{matrix} 2 & 1 & 0 \\ 3 & 1 & 2 \\ 0 & 4 & - 1 \end{matrix}],$ then $| adj (A) |$ is equal to:

Smart Achievers · Accepted Answer

(3)

Ans. 225

Explanation:

Given, $A = [\begin{matrix} 2 & 1 & 0 \\ 3 & 1 & 2 \\ 0 & 4 & - 1 \end{matrix}]$

$a d j A = [\begin{matrix} 2 & 1 & 0 \\ 3 & 1 & 2 \\ 0 & 4 & - 1 \end{matrix}]$

Now, $A = 2 (- 1 - 8) - 1 (- 3 - 0) + 0$

$= - 18 + 3$

$= - 15$

Since for a $3 \times 3$ matrix,

$| adj (A) |$ $= | A |^{3 - 1} = | A |^{2}$

we get $| adj (A) |$ $= {(- 15)}^{2} = 15^{2} = 225$

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