Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A = \(\begin{bmatrix}3 & 6\\-1 & 2 \end{bmatrix}\), then what can be said about 12\( { A }^{ -1 } \)?

Options:

12\( { A }^{ -1 } \) = 12 (adj A)

12\( { A }^{ -1 } \) = 3 (adj A)

12\( { A }^{ -1 } \) = (adj A)

12\( { A }^{ -1 } \) = 4 (adj A)

Correct Answer:

12\( { A }^{ -1 } \) = (adj A)

Explanation:

 

\( { A }^{ -1 } \) =\(\frac{adj A}{|A|}\)

But |A| = 12

So, \( { A }^{ -1 } \) =\(\frac{adj A}{12}\)

12 \( { A }^{ -1 } \) = 12 \(\frac{adj A}{12}\)

                                (adj A)