Thread: Complex Numbers- Matrices

Consider J is an element of M2(R) given by: [0 -1
1 0]
Consider the set C as a subset of M2(R) defined as : C= {aI + bJ| a,b are elements of R}
Show that the products and sums of C are again in C. Which elements of C are invertible?
Is C together with addition and multiplication of matrices a field?

Originally Posted by amm345

Consider J is an element of M2(R) given by: [0 -1
1 0]
Consider the set C as a subset of M2(R) defined as : C= {aI + bJ| a,b are elements of R}
Show that the products and sums of C are again in C. Which elements of C are invertible?
Is C together with addition and multiplication of matrices a field?

What determines whether a matrix is invertible?

Suppose that det(C) = 0. What does this tell you about a and b in relation to which elements are invertible? (just calculate det(C) and set equal to zero) This should be intuitive.