Question

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Which equation shows that the product of a square matrix A and its identity matrix I is A?

Answer 1

Option B

Explanation:

The multiplication process of matrices works by multiplying the first row of the first matrix by the first column of the second matrix. The same goes with the second row of the first matrix by the second column of the other matrix. Below is the solution why option B is the correct answer.

`A = \left[\begin{array}{ccc}8&11\\13&5\\\end{array}\right]`

`B = \left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right]` ← This is the Identity Matrix.

The attached screenshot shows the solution of the multiplication process. In essence, if you multiply any matrix by the identity (Matrix B), you should end up with your original matrix. Thus, multiplying Matrix A by the Identity matrix results in the same values as Matrix A.

Therefore, the correct answer is B.