Use the given matrices to evaluate the expression.$A=\begin{bmatrix}4&1\\-3&0\end{bmatrix}$A=[4 1−3 0]​ ,  $B=\begin{bmatrix}5&-2\\6&-1\end{bmatrix}$B=[5 −26 −1]​ ,  $C=\begin{bmatrix}1&0\\0&\ \ 1\end{bmatrix}$C=[1 00 1]​$C(AB)=$C(AB)=​

Sure, I can help with that. First, we need to multiply matrices A and B. Here's how you do it:

Step 1: Multiply A and B The product of two matrices is calculated by multiplying the elements of the first row of the first matrix with the elements of the first column of the second matrix and adding them up. This process is repeated for all rows and columns.

So, for the first element of the new matrix AB, we multiply the elements of the first row of A by the elements of the first column of B and add them up:

(45) + (16) = 20 + 6 = 26

We repeat this process for all elements of AB:

AB = [(45 + 16), (4*-2 + 1*-1); (-35 + 06), (-3*-2 + 0*-1)] = [26, -8; -15, 6]

Step 2: Multiply C and AB Now we multiply matrix C by matrix AB. The process is the same as before:

C(AB) = [(126 + 0-15), (1*-8 + 06); (026 + 1*-15), (0*-8 + 1*6)] = [26, -8; -15, 6]

So, C(AB) = [26, -8; -15, 6].