I need help with c, e, f, i, j, k. Please write legibly (8) Label each of the fo

Question

I need help with c, e, f, i, j, k. Please write legibly

(8) Label each of the following statements as True or False. Provide justification for your response. (a) True/False If A is an invertible matrix, then for any two matrices AC impliesB (b) True/False If A is invertible, then so is AB for any matrix B. (c) True/False If A and B are invertible n × n matrices, then so is AB. (d) True/False If AB is invertible, then A and B are invertible. (e) True/False If A is an invertible n × n matrix, then the equation Ax = b is consistent for any b in R". (f) True/False If A is an invertible n × n matrix, then the equation Ax b has a unique solution when it is consistent. (g) True/False If A is invertible, then so is A2. (h) True/False If A is invertible, then it reduces to the identity matrix (i) True/False If a matrix is invertible, then so is its transpose. (j) True/False If A and B are invertible n × n matrices, then A + B is invertible (k) True/False If A 0, then I A is invertible.

Explanation / Answer

answer c -----------true

e-----------true

f------------true

i-----------false

j----------true

k----------true

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