First slide

Applications of determinant

Question

A Square non singular matrix A satisfies $A^{2} - 3 A + I = 0$ then $A^{- 1} =$

Moderate

A

$\frac{1}{3} I - A$
B

$I - \frac{1}{3} A$
C

$I + \frac{1}{3} A$
D

$3 I - A$

Solution

$A^{2} - 3 A + I = 0 \Rightarrow I = 3 A - A^{2} b y r i g h t m u l t i p l i c a t i o n o f A^{- 1} \Rightarrow A^{- 1} = 3 I - A$

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