Question

If A is a square matrix such that = , then find the simplified value of
( − ) + ( − ) − .

Answer 1

Step-by-step explanation:

Apply the formula a

3

+b

3

=(a+b)

3

−3ab(a+b) in (A−I)

3

+(A+I)

3

−7A.

=((A−I)+(A+I))

3

−3(A−I)(A+I)((A−I)+(A+I))−7A

=(2A)

3

−3(A

2

−I)(2A)−7A

=8A

3

−6A

3

+6A−7A

=2A

3

–A

=2A

2

⋅A–A

=2A–A

=A