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(Strictly we would write $I_2$, to indicate the size.)</p>\n<p>$I$ plays the same role in matrix&nbsp;multiplication as the number $1$ does in number multiplication.</p>\n<p></p>\n<p>Therefore:</p>\n<p style=\"text-align: center;\">just as&nbsp; &nbsp; $a \\times 1 = 1 \\times a = a$&nbsp; &nbsp; for any number&nbsp; $a$, so&nbsp; &nbsp; $AI = IA = A$&nbsp; &nbsp; for any matrix&nbsp; &nbsp;$A$.</p>\n<p></p>", "rulesets": {}, "extensions": [], "variables": {"n1": {"name": "n1", "group": "Matrix A", "definition": "2", "description": "", "templateType": "number"}, "m1": {"name": "m1", "group": "Matrix A", "definition": "2", "description": "", "templateType": "number"}, "A1": {"name": "A1", "group": "Matrix A", "definition": "    transpose(matrix(repeat(repeat(random(0..9),m1),n1)))", "description": "", "templateType": "anything"}, "A2": {"name": "A2", "group": "Matrix A", "definition": "transpose(matrix(repeat(repeat(random(0..9),m1),n1)))", "description": "", "templateType": "anything"}, "ProdA": {"name": "ProdA", "group": "Matrix A", "definition": "{A1}{A2}", "description": "", "templateType": "anything"}, "n2": {"name": "n2", "group": "Matrix B", "definition": "3", "description": "", "templateType": "number"}, "m2": {"name": "m2", "group": "Matrix B", "definition": "3", "description": "", "templateType": "number"}, "B1": {"name": "B1", "group": "Matrix B", "definition": "transpose(matrix(repeat(repeat(random(0..9),n2),m2)))", "description": "", "templateType": "anything"}, "B2": {"name": "B2", "group": "Matrix B", "definition": "transpose(matrix(repeat(repeat(random(0..9),m2),n2)))", "description": "", "templateType": "anything"}, "ProdB": {"name": "ProdB", "group": "Matrix B", "definition": "{B1}{B2}", "description": "", "templateType": "anything"}, "n3": {"name": "n3", "group": "Matrix C", "definition": "3", "description": "", "templateType": "number"}, "m3": {"name": "m3", "group": "Matrix C", "definition": "3", "description": "", "templateType": "number"}, "C1": {"name": "C1", "group": "Matrix C", "definition": "transpose(matrix(repeat(repeat(random(0..9),n3),m3)))", "description": "", "templateType": "anything"}, "m3a": {"name": "m3a", "group": "Matrix C", "definition": "random(2..4)", "description": "", "templateType": "anything"}, "C2": {"name": "C2", "group": "Matrix C", "definition": "transpose(matrix(repeat(repeat(random(0..9),m3),m3a)))", "description": "", "templateType": "anything"}, "prodC": {"name": "prodC", "group": "Matrix C", "definition": "{C1}{C2}", "description": "", "templateType": "anything"}, "row1A": {"name": "row1A", "group": "Matrix A", "definition": "A1[0][0..1]", "description": "", "templateType": "anything"}, "I2": {"name": "I2", "group": "Ungrouped variables", "definition": "id(n1)", "description": "", "templateType": "anything"}, "I3": {"name": "I3", "group": "Ungrouped variables", "definition": "id(n2)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["I2", "I3"], "variable_groups": [{"name": "Matrix A", "variables": ["n1", "m1", "A1", "A2", "ProdA", "row1A"]}, {"name": "Matrix B", "variables": ["n2", "m2", "B1", "B2", "ProdB"]}, {"name": "Matrix C", "variables": ["n3", "m3", "C1", "m3a", "C2", "prodC"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<h4>Carry out the following multiplications:</h4>\n<p>&nbsp;</p>\n<p>$A_1 I_2=\\var{A1}\\var{I2} $</p>\n<p style=\"text-align: center;\">$A_1 I_2=$ [[0]]</p>\n<p></p>\n<p>$B_1 I_3=\\var{B1}\\var{I3}$</p>\n<p style=\"text-align: center;\">$B_1 I_3=$ [[1]]</p>\n<p style=\"text-align: left;\">&nbsp;&nbsp;</p>\n<p>$C_1 I_3=\\var{C1}\\var{I3}$</p>\n<p style=\"text-align: center;\">$C_1 I_3=$ [[2]]</p>\n<p style=\"text-align: left;\">&nbsp;</p>\n<p>$I_3 C_1=\\var{C1}\\var{I3}$</p>\n<p style=\"text-align: center;\">$I_3 C_1=$ [[3]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "{A1}", "correctAnswerFractions": false, "numRows": "{n1}", "numColumns": "{n1}", "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0}, {"type": "matrix", "useCustomName": 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