Question

If A is a square matrix such that A2 = 1, then find the simplified value of
(A-1) +(A + 1)-78.
​

Answer 1

Answer:

-77

Step by Step explanation

(A+1)+(A-1) = 2A

and 2A=1 (given)

Therefore, 1-78 = -77

Answer 2

Answer:

We have, A2 = I

Also A and I are commutative, so we can expand (A+I)n using expansion of (a+b)n, where a and b ∈ C

∴ (A-I)3 + (A+I)3 - 7A

= A3 - 3A2 + 3A - I3 + A3 + 3A2 + 3A + I3 - 7A

= 2A3 + 6A - 7A

= 2A2 . A + 6A - 7A

= 2I.A + 6A - 7A

= 2A + 6A - 7A = 8A - 7A = A

hope it helps

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