Compute the product AB where A = [ [1, 2], [3, 4] ] and B = [ [0, -1], [2, 3] ].

Compute the product AB where A = [ [1, 2], [3, 4] ] and B = [ [0, -1], [2, 3] ].

• A. [[4,5],[8,9]]
• B. [[4,7],[8,11]]
• C. [[-4,-5],[-8,-9]]
• D. [[2,3],[4,5]]

Answer: (A)

Multiplying two matrices means taking dot products of rows of the first matrix with columns of the second to form each entry. Compute AB row by row, column by column: - First row with first column: [1, 2] · [0, 2] = 1·0 + 2·2 = 4. - First row with second column: [1, 2] · [-1, 3] = 1·(-1) + 2·3 = -1 + 6 = 5. - Second row with first column: [3, 4] · [0, 2] = 3·0 + 4·2 = 8. - Second row with second column: [3, 4] · [-1, 3] = 3·(-1) + 4·3 = -3 + 12 = 9. So AB = [[4, 5], [8, 9]], which matches the correct result. Other matrices would give at least one entry that doesn’t match these four values.

Multiplying two matrices means taking dot products of rows of the first matrix with columns of the second to form each entry.

Compute AB row by row, column by column:

• First row with first column: [1, 2] · [0, 2] = 1·0 + 2·2 = 4.

• First row with second column: [1, 2] · [-1, 3] = 1·(-1) + 2·3 = -1 + 6 = 5.

• Second row with first column: [3, 4] · [0, 2] = 3·0 + 4·2 = 8.

• Second row with second column: [3, 4] · [-1, 3] = 3·(-1) + 4·3 = -3 + 12 = 9.

So AB = [[4, 5], [8, 9]], which matches the correct result. Other matrices would give at least one entry that doesn’t match these four values.