If A=[ beginmatrixx&1 1&0 endmatrix] and A=A-1, then x = ........

Question

If A=[ beginmatrixx&1 1&0 endmatrix] and A=A-1, then x = ........ (A) 0 (B) 4 (C) 2 (D) 1

Tardigrade Admin · Accepted Answer

We have, A=[x&1 1&0] ∴ |A| =(x ×0-1)= -1 adj A= [0&-1 -1&x] A-1 = (adjA/|A|) = (-1) [0&-1 -1&x] =[0&1 1&-x] Since, It is given, A = A-1 ⇒ [x&1 1&0]=[0&1 1&-x] ⇒ x=0 (By equality of matrices)

Q. If $A = [x 1 10]$ and $A = A^{- 1}$ , then $x = .......$ .

$0$

$4$

$2$

$1$

We have, $A = [x 1 10]$
$∴ ∣ A ∣ = (x \times 0 - 1) = - 1$
adj $A = [0 - 1 - 1 x]$
$A^{- 1} = \frac{a d j A}{∣ A ∣} = (- 1) [0 - 1 - 1 x] = [01 1 - x]$
Since, It is given, $A = A^{- 1}$
$\Rightarrow [x 1 10] = [01 1 - x]$
$\Rightarrow x = 0$ (By equality of matrices)

Q. If A=[x1​10​] and A=A−1, then x=........

0

4

2

1

We have, A=[x1​10​] ∴∣A∣=(x×0−1)=−1 adj A=[0−1​−1x​] A−1=∣A∣adjA​=(−1)[0−1​−1x​]=[01​1−x​] Since, It is given, A=A−1 ⇒[x1​10​]=[01​1−x​] ⇒x=0 (By equality of matrices)

Q. If $A = [x 1 10]$ and $A = A^{- 1}$ , then $x = .......$ .

$0$

$4$

$2$

$1$

We have, $A = [x 1 10]$
$∴ ∣ A ∣ = (x \times 0 - 1) = - 1$
adj $A = [0 - 1 - 1 x]$
$A^{- 1} = \frac{a d j A}{∣ A ∣} = (- 1) [0 - 1 - 1 x] = [01 1 - x]$
Since, It is given, $A = A^{- 1}$
$\Rightarrow [x 1 10] = [01 1 - x]$
$\Rightarrow x = 0$ (By equality of matrices)