Gatebook Test

Question

Comments

Answer is D?

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yes, please explain.

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Let detA be x.

Now we know that detA= det$A^{T}$=x and $\left |A A^{T} \right |=\left | A \right |\left | A^{T} \right |$

So the equation reduces to a quadratic equation: $x^{2}-3x$-4=0

Solving this equation u get the value of x as -1 and 4 respectively.

Answer 1

A and $A^T$ have same eigen values

So we can write $\lambda *\lambda -3\lambda -4=0$

The characteristic equation is $\lambda^2 -3\lambda -4=0$

on solving it we get $\lambda=4, -1$

|A|=product of eigen values=-4

option D

Answer 2

option d is the correct answer.