PrepRung
Sign inSign up free

JEE Main 2017 · Mathematics · Matrices and Determinants · easy

If A=beginbmatrix1&2\\3&4endbmatrix, then det (A^3 equals

Single correct option

If A=[1234]A=\begin{bmatrix}1&2\\3&4\end{bmatrix}, then det⁡(A3)\det(A^3) equals
  1. A. 88
  2. B. −8-8
  3. C. −6-6
  4. D. −2-2
Show answer and solution

Answer: (B) −8-8

The determinant is multiplicative: det⁡(A3)=(det⁡A)3\det(A^3)=(\det A)^3. Here det⁡A=1⋅4−2⋅3=−2\det A=1\cdot4-2\cdot3=-2, so det⁡(A3)=(−2)3=−8\det(A^3)=(-2)^3=-8. Computing A3A^3 explicitly is unnecessary. The distractor −6-6 cubes incorrectly while 88 ignores the sign of the determinant.
Report a mistake

Original question written in the JEE Main 2017 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake