Let A=[5 5 α α 0 α 5 α 0 0 5]. If |A2|=25, then |α| equals to

Question

Let A=[5 5 α α 0 α 5 α 0 0 5]. If |A2|=25, then |α| equals to (A) 52 (B) 1 (C) (1/5) (D) 5

Tardigrade Admin · Accepted Answer

Since, A=|5 5 α α 0 α 5 α 0 0 5| ∴ A2=|5 5 α α 0 α 5 α 0 0 5||5 5 α α 0 α 5 α 0 0 5| =|25 25 α+5 α2 10 α+25 α2 0 α2 5 α2+25 α 0 0 25| ⇒ |A2|=|25 25 α+5 α2 10 α+25 α2 0 α2 5 α2+25 α 0 0 25| =25|α2 5 α2+25 α 0 25|=625 α2 ∴ 625 α2=25 (given) ⇒ |α|=1 / 5

Q. Let $A = ⎣ ⎡ 500 5 α α 0 α 5 α 5 ⎦ ⎤$ . If $∣ ∣ A^{2} ∣ ∣ = 25$ , then $∣ α ∣$ equals to

$5^{2}$

1

$\frac{1}{5}$

5

Q. Let A=⎣⎡​500​5αα0​α5α5​⎦⎤​. If ∣∣​A2∣∣​=25, then ∣α∣ equals to

52

1

51​

5

Q. Let $A = ⎣ ⎡ 500 5 α α 0 α 5 α 5 ⎦ ⎤$ . If $∣ ∣ A^{2} ∣ ∣ = 25$ , then $∣ α ∣$ equals to

$5^{2}$

$\frac{1}{5}$