Q15 of 108 Page 100

If A is square matrix such that A2 = A, then (I + A) � – 7 A is equal to

Given that A2 = A

Calculating value of (I + A) � – 7 A:


⇒ I3 + A3 + 3I2A + 3IA2 – 7A


⇒ I + A2.A + 3A + 3A2 – 7A (In = I and I.A = A)


⇒ I + A.A + 3A + 3A – 7A (A2 = A)


⇒ I + A2 + 3A + 3A – 7A


⇒ I + A - A


⇒ I


Hence (I + A) � – 7 A = I.

More from this chapter

All 108 →
11

Find the matrix X so that

12

If A and B are square matrices of the same order such that AB = BA, then prove by induction that ABn = BnA. Further, prove that (AB)n = AnBn for all n ϵ N.

 13

If is such that A � = I, then

 14

If the matrix A is both symmetric and skew symmetric, then