Let A be 3- 3 matrix such that A-A -I and -A- - 1- find the value of -A-I-

Let B=A I ⇒ B '=A' I= A' A'A ⇒ B'=A'(I A) = A'B Now, |B'|=|B| = | A'B| = ( 1)^3 |A| |B| = |B| ⇒ |B| = |A I|=0 ...

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Finding Inverse Using Elementary Transformations

Let A be ...

Question

Let $A$ be $3 \times 3$ matrix such that $A^{'} A = I$ and $| A | = 1$ , find the value of $| A - I |$ .

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3 \times 3

A A^{'} = A^{'} A

B = A^{- 1} A^{'}

A

3 \times 3

a_{11} = a_{33} = 2

a_{i j} = 1

A^{- 1} = x A^{2} + y A - z I

(x + y + z)

I

3 \times 3

A A^{'} = A^{'} A

B = A^{- 1} A^{'}

A

3 \times 3

a_{11} = a_{33} = 2

a_{i j} = 1

A^{- 1} = x A^{2} + y A + z I

(x + y + z)

I

3

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