Suppose AB AC, where B and C are n × p matrices and A is invertible. Show that B = C. Is this true, in general, when A is not invertible? =

If B non singular 2 x 2 matrices and k is a non zero scalar . Which one of the following expressions is correct

Please show how to determine whether matrix A is diagonalizable: If possible, find an invertible P and a diagonal D such that P-1AP=D

Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0] 0 1 1 1 3 -1 1 • A-1 and B 2 3 1 1 0 • A8 = I3; and • 4A-((A²B)" X)" = (A²B)². T Find the matrix X.

Select all statements below which are true for all invertible n x n matrices A and B DA. AB = BA OB. (A + B)(A - B) = A² - B² Oc. (A+ A-¹)² = A²+ A-² OD. A³B2 is invertible OE. A + B is invertible OF. (In + A) (In + A-¹) = 2In + A+ A-¹