Question

Learn what an identity matrix is and about its role in matrix multiplication. ... How do you find the multiplicative inverse of a given matrix?

Answer 1

See below

Explanation:

`I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...` and so on are examples of identity matrices.

The multiplicative inverse of a 2x2 matrix is
`\displaystyle A^(-1)=(1)/(ad-bc)\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]` where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.