WHAT IS THE RELATIONSHIP BETWEEN THE **DETERMINAN**T OF A SQUARE AND INVERTIBLE MATRIX OF ORDER 3 AND ITS INVERSE? EXPLAIN HOW AND WITH EXAMPLES.

The relationship between these terms is known as , inverse of a matrix.

The inverse of an invertible square matrix *A* is given by *A*^{−1} =

Example,

If *A* =, then find *A*^{−1}.

**Solution:**

For the given matrix A, we have |*A*| = 1(3 − 2) −2 (−9 + 2) + 1 (6 − 2) = 1 + 14 + 4 = 19

Now, *A*_{11} = 1, *A*_{12} = 7, *A*_{13} = 4,

*A*_{21} = 8, *A*_{22} = −1, *A*_{23} = −6,

*A*_{31} = 3, *A*_{32} = 2, *A*_{33} = −7

∴ *adj A* =

Thus, *A*^{−1}

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