text If A - Wegin bmatrix 1 - 2 - 1110 -18 x-1 10 - 0 - 1lend bmatrix - - text then - A -4-A- 0B- IC- 2 ID- 4 I

The correct option is B I nbsp;A^2=[ 1 amp; 2 amp; 1; 0 amp; 1 amp; 1; 0 amp; 0 amp; 1 nbsp; ][ 1 amp; 2 amp; 1; 0 am ...

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Byju's Answer

Standard XII

Mathematics

Transpose of a Matrix

text If A = W...

Question

$If A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦, then A^{4} =$

0

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I

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2 I

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4 I

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Solution

The correct option is B $I$
$A^{2} = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = I A^{4} = (A^{2})^{2} = I^{2} = I$

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If A=⎡⎢⎣1210−1−1001⎤⎥⎦, then A4=

The correct option is B I A2=⎡⎢⎣1210−1−1001⎤⎥⎦⎡⎢⎣1210−1−1001⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=IA4=(A2)2=I2=I

$If A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 2 & 1 0 & - 1 & - 1 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦, then A^{4} =$