If A =squre matrix that $A^{2} = I$ , then $(A - I)^{3} + (A + Z)^{3} - 7 A$ =?

Open in App

Solution

$(A - I)^{3} + (A + I)^{3} - I A$
$A^{3} - I^{3} - 3 A I (A - I) + A^{3} + I^{3} + 3 A I (A + I) - 7 A$
$A^{2} - I - I^{3} - 3 A I (A - I) + A I + I^{3} + 33 A I (A + I) - 7 A [A^{2} = I]$
$A - I^{3} - 3 A^{2} I + 3 A I^{2} + A + I^{3} + 3 A I + 3 A I - 7 A$
$A - I - 3 I + 3 A I^{2} + A + I^{2} + 3 I^{2} + 3 A I^{2} - 7 A$
A+3A +A +3A -7A
8A -7A
A

Suggest Corrections

Similar questions

A

A^{2} = I

(A - I)^{3} + (A + I)^{3} - 7 A

A^{2} = I

(A - I)^{3} + (A + I)^{3} - 7 A

A

A^{2} = A

(I + A)^{3} - 7 A

If A is square matrix such that then is equal to

A. A B. I − A C. I D. 3A

Join BYJU'S Learning Program