If two $2 x 2$ matrices are inverses of each other, then multiplying them will result in what matrix below?
$\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]$
$\left[\begin{array}{ll}1 & 1 \\ 1 & 1\end{array}\right]$
$\left[\begin{array}{ll}0 & 1 \\ 1 & 0\end{array}\right]$
$\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$
Answer (1)
The product of two inverse matrices is the identity matrix.
The identity matrix for 2 × 2 matrices is [ 1 0 0 1 ] .
Therefore, the result of multiplying two 2 × 2 inverse matrices is the 2 × 2 identity matrix.
The final answer is [ 1 0 0 1 ] .
Explanation
Understanding Inverse Matrices When two matrices are inverses of each other, their product is the identity matrix. For 2 × 2 matrices, the identity matrix is [ 1 0 0 1 ] .
Property of Inverse Matrices The product of a matrix and its inverse is always the identity matrix.
Identifying the Correct Matrix Therefore, the correct answer is [ 1 0 0 1 ] .
Examples
In computer graphics, inverse matrices are used to undo transformations. For example, if you rotate an object by a certain angle, you can use the inverse of the rotation matrix to rotate it back to its original position. This is crucial for creating interactive and dynamic scenes where objects need to be manipulated and returned to their initial states.
