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  4. If A is involutory matrix and I is unit matrix of same order, then (I-A)(I+A) is:

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Q. If A is involutory matrix and I is unit matrix of same order, then $ (I-A)(I+A) $ is:

Bihar CECEBihar CECE 2001

Solution:

If $A$ in involutory matrix, then $A^{2}=I$
Since, $A$ is involutory matrix.
$\therefore A^{2}=I \ldots . .( i )$
Now, $(I-A)(I+A)$
$=I^{2}-A^{2}$
$=I-I [$ from (i) ]
$=0$