Q75 / 180 · COMEDK 2023 (Memory Based) · Mathematics

If $A$ is a matrix of order $4 \operatorname{such}$ that $A(\operatorname{adj} A)$ $=10 \mathrm{I}$, then $|\operatorname{adj} A|$ is equal to

  • A
    10
  • B
    100
  • Correct answer
    C
    1000
  • D
    10000

Solution

Given, $A(\operatorname{adj} A)=10 I$ We know that $A(\operatorname{adj} A)=|A| I$ $\begin{array}{ll} \therefore & 10 I=|A| I \\ \Rightarrow & |A|=10 \end{array}$ We know that $|\operatorname{adj} A|=|A|^{n-1}$, where $n$ is order of $A$ $\therefore|\operatorname{adj} A|=|A|^{4-1}=10^3=1000$

Hence, the correct answer is option: 'C'.

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