Does the following matrix A = (2 2 // 3 9) (upper row then lower row) have an inverse? If the matrix A^2 is applied as a transformation to a triangle T, by what factor will the area of the triangle change under the transformation?

The answer to the first part is that the matrix does have an inverse. This is found by finding the determinant of the matrix from the formula ad - bc (for some matrix ( a b // c d ) ) to get the answer 29 - 23 = 12. Since this is not equal to zero, the matrix has an inverse. For the second part, we know that the multiple of two matrices will have determinant equal to the product of the determinants of the two matrices, in this case 12*12 = 144 (Also allow direct computation of A^2 with matrix multiplication). The determinant is the factor by which the area of a shape will change under the transformation, so the area of triangle T will change by factor 144.