JEE MATHEMATICS MCQ: MATRICES

1 Easy

1 of 1

Application +4 | -1

A^5=O

such that

A^n \neq I

for

1 \leq n \leq 4

, then

(I-A)^{-1}

equals

View answer and explanation

Correct option: D

none of these

Option D (none of these) is correct because none of the provided options satisfy the condition for being the inverse of (I-A) given

A^5 = O

and

A^n \neq I

for

1 \leq n \leq 4

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\left|\begin{array}{ccc}1 & \left(\alpha^{2 x}-\alpha^{-2 x}\right)^2 & \left(\alpha^{2 x}+\alpha^{-2 x}\right)^2 \\ 1 & \left(\beta^{2 x}-\beta^{-2 x}\right)^2 & \left(\beta^{2 x}+\beta^{-2 x}\right)^2 \\ 1 & \left(\gamma^{2 x}-\gamma^{-2 x}\right)^2 & \left(\gamma^{2 x}+\gamma^{-2 x}\right)^2\end{array}\right|

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A

2 \times 2

A(\operatorname{adj} A)=\left[\begin{array}{cc}10 & 0 \\ 0 & 10\end{array}\right]

|A|