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Byju's Answer
Standard XII
Mathematics
Equality of Matrices
A=[ 1 2 2; 2 ...
Question

A=⎡⎢⎣122212221⎤⎥⎦⇒A3−4A2−6A=

A
0
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B
A
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C
−A
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D
1
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Solution

The correct option is B −A
Given:A=⎡⎢⎣122212221⎤⎥⎦
A2=A.A=⎡⎢⎣122212221⎤⎥⎦⎡⎢⎣122212221⎤⎥⎦
A2=⎡⎢⎣1+4+42+2+42+4+22+2+44+1+44+2+22+4+24+2+24+4+1⎤⎥⎦
A2=⎡⎢⎣988898889⎤⎥⎦
A3=A2.A=⎡⎢⎣988898889⎤⎥⎦⎡⎢⎣122212221⎤⎥⎦
=⎡⎢⎣9+16+1618+8+1618+16+88+18+1616+9+1616+18+88+16+1816+8+1816+16+9⎤⎥⎦
=⎡⎢⎣414242424142424241⎤⎥⎦
A3−4A2−6A=⎡⎢⎣414242424142424241⎤⎥⎦−4⎡⎢⎣988898889⎤⎥⎦−6⎡⎢⎣122212221⎤⎥⎦
=⎡⎢⎣414242424142424241⎤⎥⎦−⎡⎢⎣363232323632323236⎤⎥⎦−⎡⎢⎣612121261212126⎤⎥⎦
=⎡⎢⎣41−36−642−32−1242−32−1242−32−1241−36−642−32−1242−32−1242−32−1241−36−6⎤⎥⎦
=⎡⎢⎣−1−2−2−2−1−2−2−2−1⎤⎥⎦
=−⎡⎢⎣122212221⎤⎥⎦
=−A

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