Determinants
NCERT Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 2 & -3 \\ 3 & 4 \end{bmatrix}$, show that $A^2 - 6A + 17I = O$ and hence find $A^{-1}$.
Step-by-Step Solution
$A^2 - 6A + 17I = O$. Proved! [1.5 Marks]
$A^{-1} = \dfrac{1}{17}(6I - A) = \dfrac{1}{17} \begin{bmatrix} 4 & 3 \\ -3 & 2 \end{bmatrix}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Proving polynomial $A^2 - 6A + 17I = O$: 1.5 Marks
Evaluating inverse matrix $A^{-1}$: 1.5 Marks
Correct Answer:
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