Let A = - 1 2 - 3 - 2 0 3 3 - 3 1 be a matrix, then A a d j A - 1 is equal to

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Question: Answered & Verified by Expert

Let

A = [\begin{array}{l} - 1 & 2 & - 3 \\ - 2 & 0 & 3 \\ 3 & - 3 & 1 \end{array}]

be a matrix, then

|A| a d j (A^{- 1})

is equal to

MathematicsDeterminantsJEE Main

Options:

A $O_{3 \times 3}$
B $[\begin{array}{l} - 1 & 2 & - 3 \\ - 2 & 0 & 3 \\ 3 & - 3 & 1 \end{array}]$
C $I_{3}$
D $[\begin{array}{l} - 3 & - 3 & 1 \\ 3 & 0 & - 2 \\ - 1 & 2 & - 3 \end{array}]$

Solution:

2769 Upvotes Verified Answer

The correct answer is:

[\begin{array}{l} - 1 & 2 & - 3 \\ - 2 & 0 & 3 \\ 3 & - 3 & 1 \end{array}]

We know that,

A^{- 1} a d j (A^{- 1}) = |A^{- 1}| I_{3}

\Rightarrow A . A^{- 1} a d j (A^{- 1}) = |A^{- 1}| {A I}_{3}

\Rightarrow a d j (A^{- 1}) = |A^{- 1}| A

\Rightarrow |A| a d j (A^{- 1}) = A

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