Question

Matrix A=[a b ][c d] find the value of -4A+5A'

Answer 1

Answer:

AB=[1324][acbd]

=[a+2c3a+4cb+2d3b+4d]

BA=[acbd][1324]=[a+3bc+3d2a+4b2c+4d]

If given matrices are commutative then  AB=BA,

⇒a+2c=a+3b

⇒2c=3b⇒b=0

b+2d=2a+4b

⇒2a−2d=−3b

∴3b−cd−a=3b−23b23b=1