Question

A and B are two 2x2 matrices such that

A = 1 2
2 5

and

B = 5 -2
-2 1

a.) i) Find AB

Answer 1

You need to learn the general forms of matrix multiplication. Remember

only (mxn)•(nxm)= mxm is valid
Row times column, row times column....

Answer 2

keep in mind that, matrices multiplication is done by multiplying the left-row times the right-column, each row on the left matrix, will give you one row on the product matrix

thus $\bf \begin{bmatrix} 1&2\\ 2&5 \end{bmatrix}\times \begin{bmatrix} 5&-2\\ -2&1 \end{bmatrix} \\\\\\ \begin{bmatrix} (1\cdot 5)+(2\cdot -2)&\qquad (1\cdot -2)+(2\cdot 1)\\\\\\ (2\cdot 5)+(5\cdot -2)&\qquad (2\cdot -2)+(5\cdot 1) \end{bmatrix}$