If A= [ 3 3 3 3 3 3 3 3 3 ] , then A4 is equal to

Question

If A= [ 3 3 3 3 3 3 3 3 3 ] , then A4 is equal to (A) 27 A (B) 81 A (C) 243 A (D) 729 A

Tardigrade Admin · Accepted Answer

Given, A=[ beginmatrix 3 3 3 3 3 3 3 3 3 endmatrix ] ∴ A=3| beginmatrix 1 1 1 1 1 1 1 1 1 endmatrix | ∴ A2=3[ beginmatrix 1 1 1 1 1 1 1 1 1 endmatrix ].3[ beginmatrix 1 1 1 1 1 1 1 1 1 endmatrix ] =9[ beginmatrix 3 3 3 3 3 3 3 3 3 endmatrix ]=9A ∴ A4=A2.A2 =9A.9A=81A2=81.9A =729A

Q. If $A = ⎣ ⎡ 333333333 ⎦ ⎤,$ then $A^{4}$ is equal to

$27 A$

$81 A$

$243 A$

$729 A$

$3 A$

Given, $A = ⎣ ⎡ 333333333 ⎦ ⎤$
$∴$ $A = 3 ∣ ∣ 111111111 ∣ ∣$
$∴$ $A^{2} = 3 ⎣ ⎡ 111111111 ⎦ ⎤ .3 ⎣ ⎡ 111111111 ⎦ ⎤$
$= 9 ⎣ ⎡ 333333333 ⎦ ⎤ = 9 A$
$∴$ $A^{4} = A^{2} . A^{2}$
$= 9 A .9 A = 81 A^{2} = 81.9 A$
$= 729 A$

Q. If A=⎣⎡​333​333​333​⎦⎤​, then A4 is equal to

27A

81A

243A

729A

3A

Given, A=⎣⎡​333​333​333​⎦⎤​ ∴ A=3∣∣​111​111​111​∣∣​ ∴ A2=3⎣⎡​111​111​111​⎦⎤​.3⎣⎡​111​111​111​⎦⎤​ =9⎣⎡​333​333​333​⎦⎤​=9A ∴ A4=A2.A2 =9A.9A=81A2=81.9A =729A