Prove Det B = Det A for Invertible Matrix T

[aleee]

Homework Statement

if T is an invertible matrix, and A=(T^-1)B*T, prove that det B = det A

Homework Equations

A(BC) = (AB)C

The Attempt at a Solution

im not certain if inverse T and T will cancel to 1
A=B
det A = det B

 

[Matthollyw00d]

What do you know of the determinant of the product of matrices and of the determinant of inverses? Use those facts and the proof should be immediate.

 

[aleee]

oh would be it
det(A) = det(T^-1)det(BT)?

 

[Matthollyw00d]

Yes, but continue further.

 

[aleee]

oh alright, i think i got it.
det(A) = det(B)det(T)^-1det(T)
det(A) = det(B)

thanks for the help!