Determinants
NCERT Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix}$, find $A^{-1}$ and show that $A A^{-1} = I$.
Step-by-Step Solution
$|A| = -11, A^{-1} = -\dfrac{1}{11} \begin{bmatrix} 3 & -4 & -5 \\ -9 & 1 & 4 \\ -5 & 3 & 1 \end{bmatrix}$. [1.5 Marks]
$A A^{-1} = I$. Verified! [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating $|A| = -11$ and inverse matrix $A^{-1}$: 1.5 Marks
Verifying matrix product $A A^{-1} = I$: 1.5 Marks
Correct Answer:
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