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  • I need help with If then which one of the following statements is not correct ?

 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)

best_answer

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.

Posted by

divya.saini

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