Solving the Inverse Matrix Problem: Constraints and Proof

[Naome666]

Homework Statement

Let a and b be fixed constants and t be a variable. For which values of t is the matrix
A = [1 1 1 ]
[a b t ]
[a^2 b^2 t^2 ] is invertible.

Also prove that there is no real 5x5 matrix such that (A^2)+I=0

Homework Equations

The Attempt at a Solution

 

[aPhilosopher]

Interesting problem. Let me know when you've made some effort on it.

 

[Naome666]

Homework Statement

Let a and b be fixed constants and t be a variable. For which values of t is the matrix
A = [1 1 1 ]
[a b t ]
[a^2 b^2 t^2 ] is invertible.

Also prove that there is no real 5x5 matrix such that (A^2)+I=0

I don't even know where to begin this two problems!

 

[aPhilosopher]

Well, what are some conditions for a matrix to be invertible?

 

[Naome666]

Well, what are some conditions for a matrix to be invertible?

Determine (A) = 0

 

[aPhilosopher]

Cool (although you have it backwards). What conditions on t make Det(A) = 0?

 

[HallsofIvy]

determinant(A) not equal to 0. "Determine" is a verb.