Determine whether the given set of matrices under the specified operation, matrix addition or multiplication, is a
Question:
Determine whether the given set of matrices under the specified operation, matrix addition or multiplication, is a group. Recall that a diagonal matrix is a square matrix whose only nonzero entries lie on the main diagonal, from the upper left to the lower right comer. An upper-triangular matrix is a square matrix with only zero entries below the main diagonal. Associated with each n x n matrix A is a number called the determinant of A, denoted by det(A). If A and B are both n x n matrices, then det(AB) = det(A) det(B). Also, det (In) = 1 and A is invertible if and only if det(A) ≠ 0.
All n x n diagonal matrices under matrix multiplication.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Related Book For
Question Posted: