If  then which one of the following statements is not correct ?

  • Option 1)

    A^{4}-I=A^{2}+I

  • Option 2)

    A^{3}-I=A(A-I)

  • Option 3)

    A^{2}+I=A(A^{2}-I)

  • Option 4)

    A^{3}+I=A(A^{3}-I)

 

Answers (2)

Using

Multiplication of matrices -

-

 

 

A= \begin{bmatrix} 0 & -1\\ 1 & 0 \end{bmatrix}

A^{2}= \begin{bmatrix} -1 & 0\\ 0 & -1 \end{bmatrix}, A^{3} = \begin{bmatrix} 0 & 1\\ -1 & 0 \end{bmatrix},

A^{4}= \begin{bmatrix} 1 &0 \\ 0 & 1 \end{bmatrix}

For option 3,

A^{2}+I=A^{3}-AI

\begin{bmatrix} 0 & 0\\ 0& 0 \end{bmatrix}\neq \begin{bmatrix} 0 &1 \\ -1 & 0 \end{bmatrix}-\begin{bmatrix} 0 &-1 \\ 1 & 0 \end{bmatrix}\neq \begin{bmatrix} 0 & 2\\ -2 & 0 \end{bmatrix}

 


Option 1)

A^{4}-I=A^{2}+I

This option is incorrect.

Option 2)

A^{3}-I=A(A-I)

This option is incorrect.

Option 3)

A^{2}+I=A(A^{2}-I)

This option is correct.

Option 4)

A^{3}+I=A(A^{3}-I)

This option is incorrect.

N neha

Preparation Products

JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Knockout JEE Main April 2021 (Easy Installments)

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 4999/-
Buy Now
Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Knockout JEE Main January 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Exams
Articles
Questions