Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If A = \(\begin{bmatrix}13 & 5\\3 & 1 \end{bmatrix}\), then what can be said about 8\( { A }^{ -1 } \)?

Options:

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

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

8\( { A }^{ -1 } \) = 2 (adj A)

8\( { A }^{ -1 } \) = -2(adj A)

Correct Answer:

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

Explanation:

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

But |A| = -2

So, \( { A }^{ -1 } \) =\(\frac{adj A}{-2}\)

8 \( { A }^{ -1 } \) = 8 \(\frac{adj A}{-2}\)

                              =- 4 (adj A)