How do I find the matrix that satisfies an equation?
4M^2-6M=9I

What is matrix M that satisfies the equation above?

I is the identity matrix 2x2

I tried 2 ways but I'm not sure if i'm doing it correctly

I got 4 equations assuing
M= ab
cd

4a^2 + 4bc-6a=9
4ab+4db-6b=0
4ca+4dc-6c=0
4cb+4d^2-6d=9

then I tried

4M^2(M^-1) - 6M(M^-1) = 9I(M^-1)

4M - 6I = 9I(M^-1)

Question

How do I find the matrix that satisfies an equation?
4M^2-6M=9I

What is matrix M that satisfies the equation above?

I is the identity matrix 2x2 


I tried 2 ways but I'm not sure if i'm doing it correctly 

I got 4 equations assuing 
M= ab
cd

4a^2 + 4bc-6a=9
4ab+4db-6b=0
4ca+4dc-6c=0
4cb+4d^2-6d=9


then I tried 

4M^2(M^-1) - 6M(M^-1) = 9I(M^-1)

4M - 6I = 9I(M^-1)

anonymous · Answer

Do you know about eigenvalues or eigenvectors yet?

anonymous · Answer

Or what it means for two matrices to be similar?

anonymous · Answer

nope

anonymous · Answer

so far all I know are really basic stuff like inverse vectors and matrix algebra such as adding  multiplying etc

anonymous · Answer

Matrix M has row 1(ab) row2(cd)