Question

Find a 2x2 non-zero matrix A such that A^2 = 0[ Hint, try making most of the entries equal to zero]

Answer 1

To find a non-zero 2x2 matrix A such that A^2 = 0, create a matrix with most of its entries equal to zero. For example, A = [0, 1] [0, 0].

Step-by-step explanation:

To find a non-zero 2x2 matrix A such that A^2 = 0, we can create a matrix with most of its entries equal to zero. Let's consider the matrix:

A = [0, 1]
[0, 0]

To verify that A^2 = 0, we simply multiply the matrix A by itself:

A^2 = [0, 1] x [0, 1] = [0x0 + 1x0, 0x1 + 1x0] = [0, 0]

Therefore, matrix A = [0, 1] [0, 0] satisfies the condition A^2 = 0.