###### Question 22 (Textile Engineering & Fibre Science)

If the determinant and trace of a 2×2 matrix are -1 and 0 respectively, then the determinant of is

(A) | -4 |

(B) | -2 |

(C) | -1 |

(D) | 0 |

**[Show Answer]**

Option A is correct

Given-

Determinant of 2×2 matrix M is -1

As we know ,the determinant of the matrix=product of the eigen values

Let ,eigen values are a and b

So, -1=a x b

ab=-1

And

Trace of a 2×2 matrix M is 0

As we know, trace of the matix=sum of the eigen values

0=a+b

a=-b

i.e.

a x -a=-1

a=1 and b=-1

so, eigen values of matrix M are 1 & -1.

and eigen values of matrix are 1 & -1

Eigen values of matrix are (1+1) and (-1-1) i.e. 2 & -2

Determinant of =-4 (Ans)

Option A is correct.