Question

Suppose B is a (2x2) matrix such that B² = I . Show that the determinant I B I is either +1 or -1. [Hint: A²stands for the matrix product AA. I is the (2x2) identity matrix. A fact: For any two matrices E and F, I EF I = I E I I F I ]

Answer 1

Solution:-

Given that

Let B be a matrix such that

Where

I is a identity matrix of order .

That  

Determinant of I is |I| = 1

Also we know that determinant of product of two matrices

say P & Q is equal to their individual determinants

That is

|PQ| = |P| |Q|

Hence

|BB| = |B| |B| = |I|

Since

|I| = 1 so that if |B| = x,

then

x . x = 1

x = 1 or -1

Hence the determinant of B is either 1 or -1.