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JEE Main 20208 JanuaryEvening Shift
Exam
JEE Main
Year
2020
Date
8 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2020 · 8 January · Evening Shift · Mathematics · Matrices

If A = ( cases 2 & 2 9 & 4 cases ) and I = ( cases 1 & 0 0 & 1...

If A = \left(\begin{cases}2 & 2 \\ 9 & 4\end{cases}\right) and I = \left(\begin{cases}1 & 0 \\ 0 & 1\end{cases}\right), then 10A−110{A}^{- 1}, is equal to.

Options

  1. AA−4IA - 4I
  2. B6I−A6I - A
  3. CA−6IA - 6I
  4. D4I−A4I - A

Correct answer

C. A−6IA - 6I

Step-by-step solution

Characteristics equation of matrix AisA−xI=0is A - xI = 0.

\left({2294\begin{cases}2 & 2 \\ 9 & 4\end{cases}\right) - x\left({1001\begin{cases}1 & 0 \\ 0 & 1\end{cases}\right) = 0<br/><br />⇒ \left|2−x9\begin{array}{ll}2 - x \\ 9\end{array}24−x\begin{array}{ll}2 \\ 4 - x\end{array}\right| = 0 ⇒ {x}^{2} - 6x - 10 = 0</p><p></p><p>∴ {A}^{2} - 6A - 10I = 0<br/><br />10{A}^{- 1} = A - 6I$.

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