Question

The inverse of [0 1 1 0] is -​

Answer 1

Answer:

The additive inverse of 0110=110 is -110

Answer 2

Answer:

${\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] }$

Step-by-step explanation:

To find: Inverse of matrix

$A(say) = \left[\begin{array}{ccc}0&1\\1 &0\end{array}\right]$

We will use the formula

$A^{-1} = \frac{Adj (A)}{|A|}$

Determinant of the A is 0-1 = -1 ≠ 0 ⇒ A is singular, hence A is invertible matrix.

If $C_{ij}$ be the element of the cofactor matrix of A,

then by definition of the cofactor, it is easy to see that:

$C_{11} = 0\\C_{12} = -1\\C_{21} = -1\\C_{22} = 0$

Since, Adjoint of A is Transpose of the cofactor matrix of A, we have:

$Adj A = {\left[\begin{array}{ccc}0&-1\\-1&0\end{array}\right] }^T = {\left[\begin{array}{ccc}0&-1\\-1&0\end{array}\right] }\\\implies A^{-1} = \frac{ {\left[\begin{array}{ccc}0&-1\\-1&0\end{array}\right] }}{-1} = {\left[\begin{array}{ccc}0&1\\1&0\end{array}\right] }$

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