If A =[ x 1 [0.3em] 1 0 ] and A2 is the identity matrix, then x is equal to

Question

If A =[ x 1 [0.3em] 1 0 ] and A2 is the identity matrix, then x is equal to (A) -1 (B) 0 (C) 1 (D) 2

Tardigrade Admin · Accepted Answer

Given, A = [ x 1 [0.3em] 1 0 ] ∴ A2 = [ x 1 [0.3em] 1 0 ][ x 1 [0.3em] 1 0 ] = [ x2 + 1 x [0.3em] x 1 ] =[ 1 0 [0.3em] 0 1 ] (∵ A2 = I) ⇒ x2 + 1 = 1 , x = 0 ⇒ x = 0

Q. If $A = [x 1 10]$ and $A^{2}$ is the identity matrix, then x is equal to

-1

0

1

2

Given, $A = [x 1 10] ∴ A^{2} = [x 1 10] [x 1 10]$
= $[x^{2} + 1 x x 1] = [1001]$ ( $∵ A^{2}$ = I)
$\Rightarrow x^{2} + 1 = 1, x = 0 \Rightarrow x = 0$

Q. If A=[x1​10​] and A2 is the identity matrix, then x is equal to

-1

0

1

2

Given,A=[x1​10​]∴A2=[x1​10​][x1​10​] = [x2+1x​x1​]=[10​01​] (∵A2 = I) ⇒x2+1=1,x=0⇒x=0

Q. If $A = [x 1 10]$ and $A^{2}$ is the identity matrix, then x is equal to

Given, $A = [x 1 10] ∴ A^{2} = [x 1 10] [x 1 10]$
= $[x^{2} + 1 x x 1] = [1001]$ ( $∵ A^{2}$ = I)
$\Rightarrow x^{2} + 1 = 1, x = 0 \Rightarrow x = 0$