Write 5A^2 - 6A = 3I in the form AB = I and hence find A^-1 in the terms of A and I

Question

This has to do with matrices and the I is the matrix identity! Please help!!

Answer 1

Hello fellow student of Stroh, how goes it?

Anyways, to solve this problem heres what you do.

5A^2-6A=3I

5/2A^2-2A=I

A(5/2A-2I)=I

A^-1 * A (5/2A-2I) = A^-1 * I

5/2A-2I=A^-1

So as weed need to find AB=I, we know that B=A^-1 (A^-1*A*B=A^-1*I) and the above found A^-1, just multiply that by A to get your proper form.

A(5/2A-2I)=I

A     B     =I