- #1

fluidistic

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**-1. Homework Statement**

Let A and B be 2x2 matrices such that A²B=3I and A^T*B³=-I, where A^T is the transposed matrix of A, and I is the identity matrix.

Calculate det(A).

**0. The attempt at a solution**

I know I don't know how to approach correctly the problem, but I've tried something.

I know that the determinant of A squared times the determinant of B is equal to 9 and that minus the determinant of A times the determinant of B cubed is worth 1. From this, I can't reach the answer. And I've no idea about a different approach.

If you have an idea, I'd be glad to be its tester.

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