Question

What is A−1?

A=[−23−312]

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Answer 1

The inverse of square matrix A is
`A^(-1) = \left[\begin{array}{ccc}-(4)/(5) &-(1)/(5) \\(1)/(5) &(2)/(15) \end{array}\right]`.

In Mathematics and Geometry, a square matrix is a type of matrix that is composed of an equal number of both rows and columns.

In this exercise, you are required to determine the inverse of the matrix below. This ultimately implies that, we would determine the determinant of the matrix as follows;

Determinant of A = detA = (-2 × 12) - (3 × -3)

Determinant of A = detA = -24 + 9

Determinant of A = detA = -15 ≠ 0

Since the determinant of A is not equal to zero (detA ≠ 0), we can logically deduce that, the inverse of A exist;

`Adj(A) = \left[\begin{array}{ccc}12&3\\-2&1\end{array}\right] \\\\\\A^(-1) = (1)/(detA) [Adj(A)]\\\\\\A^(-1) = (1)/(-15)\left[\begin{array}{ccc}12&3\\-3&-2\end{array}\right]\\\\\\A^(-1) = \left[\begin{array}{ccc}-(4)/(5) &-(1)/(5) \\(1)/(5) &(2)/(15) \end{array}\right]`