9th class science group Math Ch no .1 Exercise no 1.5 Question no .6 part 1 complete......
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Determinant:

The determinant is a scalar value that can be computed from the elements of a square matrix. It provides a measure of the matrix's scaling effect on a vector, and it's essential in linear algebra and various mathematical applications.

A nonzero determinant indicates that the matrix is invertible.
A zero determinant indicates that the matrix is singular (noninvertible).

Multiplicative Inverse:

The multiplicative inverse, also known as the reciprocal, is a value that, when multiplied by a given number, results in 1.

For a number x, its multiplicative inverse is denoted as x^1 or 1/x.
For a matrix A, its multiplicative inverse is denoted as A^1, which satisfies the property: A × A^1 = I (identity matrix).

Note that not all matrices have a multiplicative inverse. Only square matrices with nonzero determinants have an inverse.