Let A =  and B = . If (A + B)² = A² + B², then the values of a and b are:

Concept:

Matrix Multiplication:

• Multiplication is only possible when the number of columns of the first matrix is equal to the number of rows of the second matrix.
• A m × n matrix multiplied by a n × p matrix results in a m × p matrix.
• Matrices are multiplied by multiplying each element of a row of the first m × n matrix with the corresponding elements of all the columns of the second n × p matrix to obtain the first row of the product matrix with p columns, and so on for all the m rows of the first matrix.
• For two matrices A and B, AB ≠ BA.

Calculation:

For two matrices A and B, we have:

(A + B)2 = (A + B)(A + B) = A2 + AB + BA + B2,

Since it is given that (A + B)2 = A2 + B2, we must have:

AB + BA = 0

⇒ 

⇒ 

⇒ 

Comparing the elements of equal matrices, we get:

a + 1 = 0 and b - 4 = 0.

⇒ a = -1 and b = 4.