JAMIA 2024 — Mathematics PYQ

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Question

JAMIA 2024 — Mathematics PYQ

JAMIA | Mathematics | 2024

Let $A$ be a non-singular matrix of order $2 \times 2$ , then $A^{- 1} = ?$

Choose the correct answer:

Explanation

Solution:

Hume $|A^{-1}|$ ki value nikalni hai, jahan $A$ ek $2 \times 2$ non-singular matrix hai.

Step 1: Inverse matrix ki property

Hum jaante hain ki:

A \cdot A^{-1} = I

Step 2: Dono taraf determinant lene par

|A \cdot A^{-1}| = |I|

Step 3: Determinant ki properties apply karein

$|AB| = |A| \cdot |B|$ aur $|I| = 1$ ka upyog karte hue:

|A| \cdot |A^{-1}| = 1

Step 4: $|A^{-1}|$ ki value nikaalein

|A^{-1}| = \frac{1}{|A|}

Final Answer:

\mathbf{|A^{-1}| = \frac{1}{|A|}}