If A- 2 -1- -1 2 - and I is the unit matrix of order 2- then A2 is equal to

Here, A^2=A · nbsp; A = nbsp;[ 2 amp; 1; nbsp; 1 amp; 2 ][ 2 amp; 1; nbsp; 1 amp; 2 ] =[ 5 amp; 4; nbsp; 4 amp; 5 ] No ...

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Standard IX

Mathematics

Null Matrix

If A=[ 2 -1; ...

Question

If $A = [\begin{matrix} 2 & - 1 - 1 & 2 \end{matrix}]$ and $I$ is the unit matrix of order $2,$ then $A^{2}$ is equal to

4 A - 3 I

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3 A - 4 I

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A - I

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A + I

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Solution

The correct option is A $4 A - 3 I$
Here, $A^{2} = A \cdot A = [\begin{matrix} 2 & - 1 - 1 & 2 \end{matrix}] [\begin{matrix} 2 & - 1 - 1 & 2 \end{matrix}] = [\begin{matrix} 5 & - 4 - 4 & 5 \end{matrix}]$
Now, On verifying options
$(a)$ $4 A - 3 I = 4 [\begin{matrix} 2 & - 1 - 1 & 2 \end{matrix}] - [\begin{matrix} 3 & 0 0 & 3 \end{matrix}] = [\begin{matrix} 5 & - 4 - 4 & 5 \end{matrix}]$
Thus $A^{2} = 4 A - 3 I$
We can observe that $(b), (c)$ and $(d)$ are not correct.

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Similar questions

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Null Matrix

Standard IX Mathematics

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If A=[2−1−12] and I is the unit matrix of order 2, then A2 is equal to

The correct option is A 4A−3IHere, A2=A⋅A=[2−1−12][2−1−12]=[5−4−45] Now, On verifying options (a) 4A−3I=4[2−1−12]−[3003]=[5−4−45] Thus A2=4A−3I We can observe that (b),(c) and (d) are not correct.

If $A = [\begin{matrix} 2 & - 1 - 1 & 2 \end{matrix}]$ and $I$ is the unit matrix of order $2,$ then $A^{2}$ is equal to