Question

(a 1 2)
(0 a 1)
(1 a 0)
That's a matrix. For what values of a is the matrix invertible?

Answer 1

This matrix is invertible if and only if the determinate is equal to 0.

det=a(a*0-1*a)-0(1*0-2*a)+1(1*1-2*a)
0=a(-a)-0(-2a)+1(1-2a)
0=-a^2+1-2a
0=a^2+2a-1

Using quadratic formula a=-1-sqrt(2) and a=-1+sqrt(2)

Answer 2

wow. you are smart. thank you

Answer 3

wait a second - isn't it the other way round? i.e. a matrix is invertible when the determinant is not zero.

Answer 4

You are correct, I read it wrong. So that means the matrix is invertible for all values except for the ones listed above.
If there exists a matrix B such that

\[AB=BA=I \]

I was supposed to write This matrix is not invertible if and only if the determinate is equal to 0.

Nice work :D

Answer 5

thanks again

Answer 6

Thank you!