Let A be a 3 $ \times $ 3 matrix such that A2 $-$ 5A + 7I = 0 Statement - I : A$-$1 = ${1 \over 7}$ (5I $-$ A). Statement - II : The polynomial A3 $-$ 2A2 $-$ 3A + I can be reduced to 5(A $-$ 4I). Then :

Question

Let A be a 3 $ \times $ 3 matrix such that A² $-$ 5A + 7I = 0

Statement - I :

A^$-$1 = ${1 \over 7}$ (5I $-$ A).

Statement - II :

The polynomial A³ $-$ 2A² $-$ 3A + I can be reduced to 5(A $-$ 4I).

Then :

Statement-I is true, but Statement-II is false.

Statement-I is false, but Statement-II is true.

Both the statements are true.

Both the statements are false

Solution

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