If $A$ is a square matrix with $| A | = 8$ . Find the value of $∣ ∣ A A^{- 1} ∣ ∣$ .

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Solution

Given: $| A | = 8$
$∣ ∣ A A^{- 1} ∣ ∣ = | I |$ where I is the identity matrix.
(Let $A$ be the matrix and $A^{- 1}$ be the inverse of the matrix then $A A^{- 1} = I$ )
As $| I | = 1$ hence the answer is 1.

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If A is a square matrix with |A|=8. Find the value of ∣∣AA−1∣∣.

Given:|A|=8∣∣AA−1∣∣=|I| where I is the identity matrix.(Let A be the matrix and A−1 be the inverse of the matrix then AA−1=I)As |I|=1 hence the answer is 1.

If $A$ is a square matrix with $| A | = 8$ . Find the value of $∣ ∣ A A^{- 1} ∣ ∣$ .

Given: $| A | = 8$
$∣ ∣ A A^{- 1} ∣ ∣ = | I |$ where I is the identity matrix.
(Let $A$ be the matrix and $A^{- 1}$ be the inverse of the matrix then $A A^{- 1} = I$ )
As $| I | = 1$ hence the answer is 1.