Properties of Matrix Multiplication - Inverse of a Square Matrix by the Adjoint Method

Find the adjoint of the matrices.

`[(1,2),(3,4)]`

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}- 1 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1\end{bmatrix}\]

Find x, if `[(1,2,"x"),(1,1,1),(2,1,-1)]` is singular

If A is an invertible matrix of order 2, then det (A⁻¹) is equal to ______.

Read the following passage:

Based on the above information, answer the following questions:

1. Convert the given above situation into a matrix equation of the form AX = B. (1)
2. Find | A |. (1)
3. Find A^–1. (2)
   OR
   Determine P = A² – 5A. (2)

For the matrix \[A = \begin{bmatrix}1 & 1 & 1 \\ 1 & 2 & - 3 \\ 2 & - 1 & 3\end{bmatrix}\] . Show that

Find the inverse by using elementary row transformations:

\[\begin{bmatrix}3 & 10 \\ 2 & 7\end{bmatrix}\]

If \[\begin{bmatrix}1 & - \tan \theta \\ \tan \theta & 1\end{bmatrix} \begin{bmatrix}1 & \tan \theta \\ - \tan \theta & 1\end{bmatrix} - 1 = \begin{bmatrix}a & - b \\ b & a\end{bmatrix}\], then _______________ .