Determinants
NCERT Class 12
CBSE
Grade 12
Question:
If $A = \begin{bmatrix} 1 & \tan x \\ -\tan x & 1 \end{bmatrix}$, show that $A' A^{-1} = \begin{bmatrix} \cos 2x & -\sin 2x \\ \sin 2x & \cos 2x \end{bmatrix}$.
Step-by-Step Solution
$A^{-1} = \cos^2 x \begin{bmatrix} 1 & -\tan x \\ \tan x & 1 \end{bmatrix}$. [1.0 Mark]
$A' A^{-1} = \begin{bmatrix} \cos 2x & -\sin 2x \\ \sin 2x & \cos 2x \end{bmatrix}$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating inverse matrix $A^{-1}$: 1.0 Mark
Evaluating product $A' A^{-1}$: 1.0 Mark
Correct Answer:
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