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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
MCQ
Evaluate $ |\text{A}|^2-5|\text{A}|+1,$ if $\text{A}=\begin{bmatrix}7&4\\5&5\end{bmatrix}$ is:
  • A
    $161$
  • B
    $251$
  • C
    $150$
  • ✓
    $151$
✓

Answer

Correct option: D.
$151$
Given that, $\text{A}=\begin{bmatrix}7&4\\5&5\end{bmatrix}$
$|\text{A}|=(7(5)-5(4))$
$=35-20$
$=15$
$|\text{A}|^2-5|\text{A}|+1$
$=(15)^2-5(15)+1$
$=225-75+1$
$=151.$

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