- #1

- 9

- 1

Find a 2 x 2 matrix A such that A

^{2}= ##\begin{pmatrix} -1 & 0 \\ 0 & -1 \\ \end{pmatrix}## = -I

The solution is available in the answer section of the book, but it is not shown how the author comes up with the solution.

My initial attempt at the problem involved multiplying both sides of the equation by the inverse of A in attempt to isolate A, that only produced IA=-A

^{-1}which is really no more clear than what I started with.

I then attempted to express A as ##\begin{pmatrix} a & b \\ c & d \\ \end{pmatrix}## such that A

^{2}= ##\begin{pmatrix} a^2+bc & ab+bd \\ ca+dc & cb + d^2 \\ \end{pmatrix}##=-I, but it this didn't lead me anywhere either.

This section hasn't introduced to determinants so I certain that isn't a part of the approach. What am I missing?

Thanks.