Plz fast question 1 Q 1 If A=α22α and A3=125, α is equal to (a) ±2 (b) ±3 (c) - Maths - Matrices

Question

Plz fast question 1
Q 1 If A = α 2 2 α   a n d   A 3 = 125 ,  
α is equal to
(a) ± 2
(b) ± 3
(c) ± 5
(d) 0

Neha Sethi · Accepted Answer

Dear student
We have,A=α22αA2=α22αα22α=α2+42α+2α2α+2α4+α2=α2+44α4αα2+4Now, A3=A2
A=α2+44α4αα2+4α22α=α3+4α+8α8+2α2+4α24α2+8+2α24α+8α+α3=α3+12α6α2+86α2+8α3+12αNow, given that A3=125and A3=α3+12α2-6α2+82ie
α3+12α2-6α2+82=125α6+144α2+24α4-36α4-64-96α2-125=0α6+48α2-12α4-189=0Take w=α2So, w3-12w2+48w-189=0w-9w2-3w+21=0w-9=0 or w2-3w+21=0  Rejected no solution for x∈R as per options mentioned in the question   w=9 α2=9α=±3
Regards

Plz fast question 1 Q.1. If A = α 2 2 α a n d A 3 = 125 , α is equal to (a) ± 2 (b) ± 3 (c) ± 5 (d) 0

Plz fast question 1
Q.1. If $A = [\begin{matrix} α & 2 \\ 2 & α \end{matrix}] a n d |A^{3}| = 125, α$ is equal to
(a) $\pm$ 2
(b) $\pm$ 3
(c) $\pm$ 5
(d) 0